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JEE Matrices PYQs with Solutions

506 previous year questions from Matrices (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

506 questionsMathematics2006–2026Answers + solutions

About Matrices PYQs

Matrices has 506 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (179) and JEE Advanced (41), spanning 2006 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 26
  • 2025: 23
  • 2024: 22
  • 2023: 31
  • 2022: 34
  • 2021: 34
  • 2020: 13
  • 2019: 12
  • 2018: 2
  • 2017: 1
  • 2016: 3
  • 2015: 1

Matrices questions with solutions

1

Which one of the following matrices can be obtained by performing elementary row transformations on the 3 × 3 identity matrix?

JEE Advanced 2026 Solution View → 2

Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be integers such that M^ 26 = bmatrix p & q r & s bmatrix and ∑_ k=1 ^ 26 M^k = bmatrix a & b

JEE Advanced 2026 Solution View → 3

For real numbers α, β, γ, δ and μ , consider the matrix M = bmatrix α & 1 2 & - 1 2 1 3 & β & 1 3 γ & δ & μ bmatrix . Suppose that MM^T = I , where M^T is the transpose of the

JEE Advanced 2026 Solution View → 4

Let ℝ denote the set of all real numbers and let i = -1 . Consider the matrices S = bmatrix 0 & -1 1 & 0 bmatrix and T = bmatrix 1 & 1 0 & 1 bmatrix . Let a, b, c, d be real

JEE Advanced 2026 Solution View → 5

Let A = bmatrix α & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5α & 0 0 & 4α & -2α bmatrix + adj(A) . If (B)=66 , then (adj(A)) equals:

JEE Main 2026 Solution View → 6

Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 ≤ i, j ≤ 3 . If B = A^ 99 - I , then the value of b_ 31 - b_ 21 b_ 32 is :

JEE Main 2026 Solution View → 7

Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + α(adj(adj(A))) + β(adj(A)(adj(adj(A)))) = bmatrix 2 & -2 & 2 -2 & 0 & -1 0 & 0 & -1 bmatrix for some α, β ∈ ℝ

JEE Main 2026 Solution View → 8

Let M be a 3 × 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix and M pmatrix 0 0 1 pmatrix = pmatrix -1 1 1

JEE Main 2026 Solution View → 9

Let A be a 3 × 3 matrix such that A^T bmatrix 1 0 1 bmatrix = bmatrix 5 2 2 bmatrix , A^T bmatrix 0 0 1 bmatrix = bmatrix 3 1 1 bmatrix , A bmatrix 1 0 1 bmatrix = bmatrix 3 4 4

JEE Main 2026 Solution View → 10

Let A= bmatrix 1 & 2 & 7 4 & -2 & 8 3 & 8 & -7 bmatrix and (A-α I)=0 , where α is a real number. If the largest possible value of α is p , then the circle (x-p)^2+(y-2p)^2=320

JEE Main 2026 Solution View → 11

Let S = \ A = bmatrix a & b c & d bmatrix : a, b, c, d ∈ \ 0, 1, 2, 3, 4\ and A^2 - 4A + 3I = 0\ be a set of 2 × 2 matrices. Then the number of matrices in S , for which the sum

JEE Main 2026 Solution View → 12

Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of the matrix adj(adj(2(adjA)^ -1 )) is equal to:

JEE Main 2026 Solution View → 13

Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3 bmatrix . If matrices P and Q are such that PA = B and AQ = B , then the absolute value of the

JEE Main 2026 Solution View → 14

Let A = bmatrix 1 & 2 1 & α bmatrix and B = bmatrix 3 & 3 β & 2 bmatrix . If A^2 - 4A + I = O and B^2 - 5B - 6I = O , then among the two statements : (S1): [(B-A)(B+A)]^T =

JEE Main 2026 Solution View → 15

Let A=[ array ll 3 & -4 1 & -1 array ] and B be two matrices such that A^ 100 =100 B+I . Then the sum of all the elements of B^ 100 is \_\_\_\_

JEE Main 2026 Solution View → 16

Let A, B and C be three 2 × 2 matrices with real entries such that B=(I+A)^ -1 and A+C=I . If BC=[ array cc 1 & -5 -1 & 2 array ] and CB[ array l x_ 1 x_ 2 array ]=[ array c 12 -6

JEE Main 2026 Solution View → 17

Let f(x)=∫ 7 x^ 10 +9 x^ 8 (1+x^ 2 +2 x^ 9 )^ 2 d x, x>0, _ x arrow 0 f(x)=0 and f(1)=(1)/(4) . If A=[ array ccc 0 & 0 & 1 (1)/(4) & f^ (1) & 1 α^ 2 & 4 & 1 array ] and B=adj(adj

JEE Main 2026 Solution View → 18

Let P=[p_ i j ] and Q=[q_ i j ] be two square matrices of order 3 such that q_ ij =2^ (i+j-1) p_ ij and det(Q)=2^ 10 . Then the value of det(adj(adj P)) is:

JEE Main 2026 Solution View → 19

The number of 3 × 2 matrices A, which can be formed using the elements of the set \ -2,-1,0,1,2\ such that the sum of all the diagonal elements of A^ T A is 5, is

JEE Main 2026 Solution View → 20

Let A=[ array ccc 0 & 2 & -3 -2 & 0 & 1 3 & -1 & 0 array ] and B be a matrix such that B(I-A)=I+A . Then the sum of the diagonal elements of B^ T B is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 21

Let |A|=6 , where A is a 3 × 3 matrix. If |adj(3 adj(~A^ 2 · adj(2 ~A)))|=2^ m · 3^ n , m, n ∈ N , then m+n is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 22

If X=[ array l x y z array ] is a solution of the system of equations A X=B , where adj A=[ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] and B=[ array l 4 0 2 array ] , then

JEE Main 2026 Solution View → 23

If A=[ array ll 2 & 3 3 & 5 array ] , then the determinant of the matrix (A^ 2025 -3 ~A^ 2024 +A^ 2023 ) is

JEE Main 2026 Solution View → 24

Let A be a 3 × 3 matrix such that A+A^ T =O . If A[ array c 1 -1 0 array ]=[ array l 3 3 2 array ], A^ 2 [ array c 1 -1 0 array ]=[ array c -3 19 -24 array ] and det(adj(2

JEE Main 2026 Solution View → 25

For the matrices A=[ array ll 3 & -4 1 & -1 array ] and B=[ array ll -29 & 49 -13 & 18 array ] , if (A^ 15 +B)[ array l x y array ]=[ array l 0 0 array ] , then among the

JEE Main 2026 Solution View → 26

For some α, β ∈ R , let A=[ array ll α & 2 1 & 2 array ] and B=[ array ll 1 & 1 1 & β array ] be such that A^ 2 -4 A+2 I=B^ 2 -3 B+I=O . Then (det(adj(A^ 3 -B^ 3 )))^ 2 is equal

JEE Main 2026 Solution View → 27

Consider the matrix, P=( array lll 2 & 0 & 0 0 & 2 & 0 0 & 0 & 3 array ) Let the transpose of a matrix X be denoted by X^T . Then the number of 3 × 3 invertible matrices Q with

JEE Advanced 2025 Solution View → 28

Let I=( array ll 1 & 0 0 & 1 array ) and P=( array ll 2 & 0 0 & 3 array ) . Let Q=( array ll x & y z & 4 array ) for some non-zero real numbers x, y , and z , for which there is 2

JEE Advanced 2025 Solution View → 29

Let α be a solution of x^2+x+1=0 , and for some a and b in ℝ,[ array lll 4 & a & b array ][ array ccc 1 & 16 & 13 -1 & -1 & 2 -2 & -14 & -8 array ]=[ array ccc 0 & 0 & 0 array ] .

JEE Main 2025 Solution View → 30

Let A=[ array ccc 2 & 2+p & 2+p+q 4 & 6+2 p & 8+3 p+2 q 6 & 12+3 p & 20+6 p+3 q array ] . If det(adj(adj(3 ~A)))=2^ m · 3^ n , m, n ∈ N , then m+n is equal to

JEE Main 2025 Solution View → 31

The number of singular matrices of order 2 , whose elements are from the set \ 2,3,6,9\ is

JEE Main 2025 Solution View → 32

Let A be a 3 × 3 matrix such that aligned & |adj(adj(adj A))|=81 . If & S=\ n ∈ ℤ:(|adj(adj A)|)^ ((n-1)^2)/(2) =|A|^ (3 n^2-5 n-4) \ aligned , then ∑_ n ∈ S |A^ (n^2+n) | is

JEE Main 2025 Solution View → 33

Let the matrix A=[ array lll 1 & 0 & 0 1 & 0 & 1 0 & 1 & 0 array ] satisfy A^n=A^ n-2 +A^2-I for n ≥ 3 . Then the sum of all the elements of A^ 50 is :-

JEE Main 2025 Solution View → 34

Let A=[ array ccc θ & 0 & - θ 0 & 1 & 0 θ & 0 & θ array ] . If for some θ ∈(0, π) , A^2=A^T , then the sum of the diagonal elements of the matrix (A+I)^3+(A-I)^3-6 ~A is equal to

JEE Main 2025 Solution View → 35

Let I be the identity matrix of order 3 × 3 and for the matrix A=[ array ccc λ & 2 & 3 4 & 5 & 6 7 & -1 & 2 array ],|A|=-1 . Let B be the inverse of the matrix adj(A adj(A^2)) .

JEE Main 2025 Solution View → 36

Let A be a matrix of order 3 × 3 and |A|=5 . If |2 adj(3 ~A adj(2 ~A))|=2^α · 3^β · 5^γ α, β, γ ∈ N then α+β+γ is equal to

JEE Main 2025 Solution View → 37

Let A be a 3 × 3 real matrix such that A^2(A-2 I)- 4(~A-I)=O , where I and O are the identity and null matrices, respectively. If A^5=α A^2+β A+γ I , where α, β and γ are real

JEE Main 2025 Solution View → 38

Let A=[ array cc α & -1 6 & β array ], α 0 , such that det(A)=0 and α+β=1 . If I denotes 2 × 2 identity matrix, then the matrix (1+A)^8 is:

JEE Main 2025 Solution View → 39

Let a ∈ R and A be a matrix of order 3 × 3 such that det(A)=-4 and A+I=[ array lll 1 & a & 1 2 & 1 & 0 a & 1 & 2 array ] , where I is the identity matrix of order 3 × 3 . If

JEE Main 2025 Solution View → 40

Let A=[a_ i j ] be a matrix of order 3 × 3 , with a_ i j =( 2 )^ i+j . If the sum of all the elements in the third row of A^2 is α+β 2 , α, β ∈ Z , then α+β is equal to :

JEE Main 2025 Solution View → 41

Let \(A=[a_ i j ]=[ array cc _ 5 128 & _4 5 _5 8 & _4 25 array ]\). If \(A_ i j \) is the cofactor of \(a_ i j , C_ i j =∑_ k=1 ^ 2 a_ i k A_ j k , 1 ≤ i, j ≤ 2\), and \(C= [C_ i

JEE Main 2025 Solution View → 42

Let \( S=\ m ∈ Z : A^ m^ 2 +A^ m =3 I-A^ -6 \ \), where \( A=[ array cc 2 & -1 1 & 0 array ]\). Then \( n(S) \) is equal to ______.

JEE Main 2025 Solution View → 43

Let A=[ array cc 1 2 & -2 0 & 1 array ] and P=[ array cc θ & - θ θ & θ array ], θ 0 . If B=PAP^ T , C=P^ T B^ 10 P and the sum of the diagonal elements of C is m n , where gcd(m

JEE Main 2025 Solution View → 44

Let M denote the set of all real matrices of order 3 × 3 and let S=\ -3,-2,-1,1,2\ . Let aligned & S_ 1 =\ A=[a_ ij ] ∈ M: A=A^ T and a_ ij ∈ S, ∀ i, j\ , & S _ 2 =\ A=[a_ ij ] ∈

JEE Main 2025 Solution View → 45

Let A be a 3 × 3 matrix such that X^T A X=O for all nonzero 3 × 1 matrices X=[ array l x y z array ] . If A[ array l 1 1 1 array ]=[ array c 1 4 -5 array ], A[ array l 1 2 1 array

JEE Main 2025 Solution View → 46

Let A=[a_ i j ] be 3 × 3 matrix such that A[ array l 0 1 0 array ]=[ array l 0 0 1 array ], A[ array l 4 1 3 array ]=[ array l 0 1 0 array ] and A[ array l 2 1 2 array ]=[ array l

JEE Main 2025 Solution View → 47

If A, B , and (adj(A^ -1 )+adj(B^ -1 )) are non-singular matrices of same order, then the inverse of A(adj(A^ -1 )+adj(B^ -1 ))^ -1 ~B , is equal to

JEE Main 2025 Solution View → 48

For a 3 × 3 matrix M , let trace (M) denote the sum of all the diagonal elements of M . Let A be a 3 × 3 matrix such that |A|=(1)/(2) and trace (A)=3 . If B=adj(adj(2 A)) , then

JEE Main 2025 Solution View → 49

Let A be a square matrix of order 3 such that det(A)=-2 and det(3 adj(-6 adj(3 A)))=2^ m+n · 3^ mn , m . Then 4 ~m+2 n is equal to _______

JEE Main 2025 Solution View → 50

Let α and β be the distinct roots of the equation x^2+x-1=0 . Consider the set T=\ 1, α, β\ . For a 3 × 3 matrix M=(a_ i j )_ 3 × 3 , define R_i=a_ i 1 +a_ i 2 +a_ i 3 and C_j=a_

JEE Advanced 2024 Solution View → 51

Let B=[ array ll 1 & 3 1 & 5 array ] and A be a 2 × 2 matrix such that A B^ -1 =A^ -1 . If B C B^ -1 =A and C^4+α C^2+β I=O , then 2 β-α is equal to

JEE Main 2024 Solution View → 52

Let A be a non-singular matrix of order 3 . If det(3 adj(2 adj((det A) A)))=3^ -13 · 2^ -10 and det(3 adj(2 ~A))=2^ m · 3^ n , then |3 ~m+2 n| is equal to

JEE Main 2024 Solution View → 53

Let A=[ array lll 2 & a & 0 1 & 3 & 1 0 & 5 & b array ] . If A^3=4 A^2-A-21 I , where I is the identity matrix of order 3 × 3 , then 2 a+3 b is equal to

JEE Main 2024 Solution View → 54

Let A=[ array cc 2 & -1 1 & 1 array ] . If the sum of the diagonal elements of A^ 13 is 3^n , then n is equal to_________

JEE Main 2024 Solution View → 55

If A is a square matrix of order 3 such that det(A)=3 and det(adj(-4 adj(-3 adj(3 adj((2 ~A)^ -1 )))))=2^ m 3^ n , then m+2 n is equal to :

JEE Main 2024 Solution View → 56

Let α β ≠ 0 and A=[ array rrr β & α & 3 α & α & β -β & α & 2 α array ] . If B=[ array rrr 3 α & -9 & 3 α -α & 7 & -2 α -2 α & 5 & -2 β array ] is the matrix of cofactors of the

JEE Main 2024 Solution View → 57

Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2 . Then |A^ T A(adj(2 ~A))^ -1 (adj(4 ~B))(adj(AB))^ -1 AA^ T | is equal to :

JEE Main 2024 Solution View → 58

Let A=[ array ll 1 & 2 0 & 1 array ] and B=I+adj(A)+(adj A)^2+…+(adj A)^ 10 . Then, the sum of all the elements of the matrix B is:

JEE Main 2024 Solution View → 59

Let A be a 2 × 2 symmetric matrix such that A[ array l 1 1 array ]=[ array l 3 7 array ] and the determinant of A be 1 . If A^ -1 =α A+β I , where I is an identity matrix of order

JEE Main 2024 Solution View → 60

Let α ∈(0, ∞) and A=[ array lll 1 & 2 & α 1 & 0 & 1 0 & 1 & 2 array ] . If det(adj(2 A-A^T) · adj(A-2 A^T))=2^8 , then (det(A))^2 is equal to:

JEE Main 2024 Solution View → 61

Let A be a 3 × 3 matrix of non-negative real elements such that A[ array l 1 1 1 array ]=3[ array l 1 1 1 array ] . Then the maximum value of det(A) is ______

JEE Main 2024 Solution View → 62

Let A = I _ 2 - 2M M ^ T , where M is real matrix of order 2 × 1 such that the relation M ^ T M = I _ 1 holds. If λ is a real number such that the relation AX = holds for some

JEE Main 2024 Solution View → 63

If A = [ cases 2 & 1 - 1 & 2 cases ], B[ cases 1 & 0 1 & 1 cases ], C = AB A ^ T and X = A ^ T C ^ 2 A , then det X is equal to:

JEE Main 2024 Solution View → 64

Let A be a 3 × 3 matrix and det(A) = 2 . If n = det( adj(adj(. ... (adjA)))) _ ⏟ _ 2024 - times ) , then the remainder when n is divided by 9 is equal to __________.

JEE Main 2024 Solution View → 65

Let R = ( cases x & 0 & 0 0 & y & 0 0 & 0 & z cases ) be a non-zero 3 × 3 matrix, where xsinθ = ysin(θ + (2π)/(3)) = zsin(θ + (4π)/(3)) ≠ 0, θ ∈ ( 0, 2π ) . For a square matrix M

JEE Main 2024 Solution View → 66

Let A = [ cases 2 & 1 & 2 6 & 2 & 11 3 & 3 & 2 cases ] and P = [ cases 1 & 2 & 0 5 & 0 & 2 7 & 1 & 5 cases ] . The sum of the prime factors of | P ^ - 1 AP - 2I| is equal to

JEE Main 2024 Solution View → 67

Let A = [ cases 1 & 0 & 0 0 & α & β 0 & β & α cases ] and | 2A | ^ 3 = 2 ^ 21 where α, β ∈ Z , Then a value of α is

JEE Main 2024 Solution View → 68

Let A be a square matrix such that AA ^ T = I . Then (1)/(2)A[ (A + A ^ T ) ^ 2 + (A - A ^ T ) ^ 2 ] is equal to

JEE Main 2024 Solution View → 69

Let A be a 2 × 2 real matrix and I be the identity matrix of order 2 . If the roots of the equation | A - xI | = 0 be - 1 and 3, then the sum of the diagonal elements of the

JEE Main 2024 Solution View → 70

Let A = [ cases 2 & 0 & 1 1 & 1 & 0 1 & 0 & 1 cases ], B = [ cases B _ 1 & B _ 2 & B _ 3 cases ] , where B _ 1 , B _ 2 , B _ 3 are column matrices, and AB _ 1 = [ array ll 1 0 0

JEE Main 2024 Solution View → 71

Consider the matrix f(x) = [ cases cosx & - sinx & 0 sinx & cosx & 0 0 & 0 & 1 cases ] . Given below are two statements : Statement I: f ( - x ) is the inverse of the matrix f ( x

JEE Main 2024 Solution View → 72

Let M = ( a _ ij ), i, j ∈ 1, 2, 3 , be the 3 × 3 matrix such that a _ ij = 1 if j + 1 is divisible by i , otherwise a _ ij = 0 . Then which of the following statements is(are)

JEE Advanced 2023 Solution View → 73

Let R = \ ( cases a & 3 & b c & 2 & d 0 & 5 & 0 cases ): a, b, c, d ∈ \ 0, 3, 5, 7, 11, 13, 17, 19\ \ . Then the number of invertible matrices in R is

JEE Advanced 2023 Solution View → 74

Let the determinant of a square matrix A of order m be m - n , where m and n satisfy 4m + n = 22 and 17m + 4n = 93 . If det(nadj(adj(mA))) = 3 ^ a 5 ^ b 6 ^ c , then a + b + c is

JEE Main 2023 Solution View → 75

Let for A = [ cases 1 & 2 & 3 α & 3 & 1 1 & 1 & 2 cases ], |A| = 2 . If | 2 adj ( 2 adj ( 2A ) ) | = 32 ^ n , then 3n + α is equal to

JEE Main 2023 Solution View → 76

The number of symmetric matrices of order 3, with all the entries from the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is

JEE Main 2023 Solution View → 77

Let B = [ cases 1 & 3 & α 1 & 2 & 3 α & α & 4 cases ], α > 2 be the adjoint of a matrix A and |A| = 2 . Then [ cases α & - 2α & α cases ]B[ array ll α - 2α α array ] is equal to

JEE Main 2023 Solution View → 78

Let A = [ cases 1 & (1)/(51) 0 & 1 cases ] . If B = [ cases 1 & 2 - 1 & - 1 cases ]A[ cases - 1 & - 2 1 & 1 cases ] , then the sum of all the elements of the matrix ∑ _ n = 1 ^ 50

JEE Main 2023 Solution View → 79

Let A = [ cases 0 & 1 & 2 a & 0 & 3 1 & c & 0 cases ] , where a, c ∈ R . If A ^ 3 = A and the positive value of a belongs to the interval ( n - 1, n ] , where n ∈ ℕ , then n is

JEE Main 2023 Solution View → 80

Let A be a 2 × 2 matrix with real entries such that A ^ ' = + 1, where α ∈ ℝ -\ - 1, 1\ ., If det ( A ^ 2 - A) = 4 , the sum of all possible values of α is equal to

JEE Main 2023 Solution View → 81

If A = (1)/(5 ! 6 ! 7 !)[ cases 5 ! & 6 ! & 7 ! 6 ! & 7 ! & 8 ! 7 ! & 8 ! & 9 ! cases ] , then |adj (adj (2A))| is equal to

JEE Main 2023 Solution View → 82

If A is a 3 × 3 matrix and |A| = 2 , then |3 adj (|3A| A ^ 2 )| is equal to

JEE Main 2023 Solution View → 83

If A = [ cases 1 & 5 λ & 10 cases ], A ^ - 1 = + and α + β = - 2 , then 4 α ^ 2 + β ^ 2 + λ ^ 2 is equal to :

JEE Main 2023 Solution View → 84

Let [ array ll 2 1 0 array array ll 1 2 - 1 array array ll 0 - 1 2 array ] . If |adj ( adj(adj2A ))| = ( 16 ) ^ n , then n is equal to

JEE Main 2023 Solution View → 85

Let P = [ cases 3 2 & (1)/(2) - (1)/(2) & 3 2 cases ], A = [ cases 1 & 1 0 & 1 cases ] and Q = PA P ^ T . If P ^ T Q ^ 2007 P = [ cases a & b c & d cases ] then 2a + b - 3c - 4d

JEE Main 2023 Solution View → 86

Let P be a square matrix such that P ^ 2 = I - P . For α, β, γ, δ ∈ ℕ , if P ^ α + P ^ β = - 29P and P ^ α - P ^ β = - 13P , then α + β + γ - δ is equal to

JEE Main 2023 Solution View → 87

Let A = [ a _ ij ] _ 2 × 2 , where a ≠ ij 0 for all i, j and A ^ 2 = I , Let a be the sum of all diagonal elements of A and b = |A| Then 3 a ^ 2 + 4 b ^ 2 is equal to

JEE Main 2023 Solution View → 88

If A = (1)/(2)[ cases 1 & 3 - 3 & 1 cases ] then,

JEE Main 2023 Solution View → 89

Let A = ⌊ a _ ^ i ^ j ⌋ · a _ ij ∈ Z ∩ [0, 4], 1 ≤ i, j ≤ 2 . The number of matrices A such that the sum of all entries is a prime number p ∈ (2, 13) is _____ .

JEE Main 2023 Solution View → 90

Let A be a n × n matrix such that |A| = 2 . If the determinant of the matrix Adj (2 . Adj (2 A ^ - 1 )) is 2 ^ 84 , then n is equal to _____ .

JEE Main 2023 Solution View → 91

Let A = [ cases 1 & 0 & 0 0 & 4 & - 1 0 & 12 & - 3 cases ] . Then the sum of the diagonal elements of the matrix (A + I) ^ 11 is equal to:

JEE Main 2023 Solution View → 92

If P is a 3 × 3 real matrix such that P ^ T = aP + ( a - 1 ) I , where a > 1 , then

JEE Main 2023 Solution View → 93

Let A = [ cases m & n p & q cases ], d = |A| ≠ 0 and |A - d(Adj A)| = 0 . Then

JEE Main 2023 Solution View → 94

The set of all values of t ∈ ℝ , for which the matrix [ cases e ^ t & e ^ - t (sint - 2cost) & e ^ - t (- 2sint - cost) e ^ t & e ^ - t (2sint + cost) & e ^ - t (sint - 2cost) e ^

JEE Main 2023 Solution View → 95

Let A be a symmetric matrix such that |A| = 2 and [ cases 2 & 1 3 &(3)/(2) cases ] A = [ cases 1 & 2 α & β cases ] If the sum of the diagonal elements of A is s , then α ^ 2 is

JEE Main 2023 Solution View → 96

Let α and β be real numbers. Consider a 3 × 3 matrix A such that A ^ 2 = 3A + . If A ^ 4 = 21A + , then

JEE Main 2023 Solution View → 97

Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements (S1) A ^ 13 B ^ 26 - B ^ 26 A ^ 13 is symmetric (S2) A ^ 26 C ^ 13

JEE Main 2023 Solution View → 98

Let A = [ cases 1 10 & 3 10 - 3 10 & 1 10 cases ] and B = [ cases 1 & - i 0 & 1 cases ] , where i = - 1 . If M = A ^ T BA , then the inverse of the matrix AM ^ 2023 A ^ T is

JEE Main 2023 Solution View → 99

Let x, y, z > 1 and A = [ cases 1 & _ x y & _ x z _ y x & 2 & _ y z _ z x & _ z y & 3 cases ] . Then |adj (adj A ^ 2 )| is equal to

JEE Main 2023 Solution View → 100

The number of square matrices of order 5 with entries from the set 0, 1 , such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is

JEE Main 2023 Solution View → 101

Let A be a 3 × 3 matrix such that |adj(adj(adj . A))| = 12 ^ 4 . Then | A ^ - 1 adjA| is equal to

JEE Main 2023 Solution View → 102

If A and B are two non-zero n × n matrices such that A ^ 2 + B = A ^ 2 B, then

JEE Main 2023 Solution View → 103

Let β be a real number. Consider the matrix A = ( cases β & 0 & 1 2 & 1 & - 2 3 & 1 & - 2 cases ) . If A ^ 7 - (β - 1) A ^ 6 - β A ^ 5 is a singular matrix, then the value of 9β

JEE Advanced 2022 Solution View → 104

If M = ( cases (5)/(2) & (3)/(2) - (3)/(2) & - (1)/(2) cases ) , then which of the following matrices is equal to M ^ 2022 ?

JEE Advanced 2022 Solution View → 105

Which of the following matrices can NOT be obtained from the matrix [ cases - 1 & 2 1 & - 1 cases ] by a single elementary row operation?

JEE Main 2022 Solution View → 106

Let x = [ array ll 1 1 1 array ] and A = [ cases - 1 & 2 & 3 0 & 1 & 6 0 & 0 & - 1 cases ] . For k ∈ ℕ , if X ^ ' A ^ k X = 33 , then k is equal to

JEE Main 2022 Solution View → 107

Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Then

JEE Main 2022 Solution View → 108

The number of matrices of order 3 × 3 , whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _______.

JEE Main 2022 Solution View → 109

Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

JEE Main 2022 Solution View → 110

Let the matrix A = [ cases 0 & 1 & 0 1 & 0 & 0 0 & 0 & 1 cases ] and the matrix B _ 0 = A ^ 49 + 2 A ^ 98 . If B _ n = Adj( B _ n - 1 ) for all n ≥ 1 , then det ( B _ 4 ) is equal

JEE Main 2022 Solution View → 111

Let A = [ cases 1 & - 1 2 & α cases ] and B = [ cases β & 1 1 & 0 cases ], α, β ∈ R . Let α _ 1 be the value of α which satisfies (A + B) ^ 2 = A ^ 2 + [ cases 2 & 2 2 & 2 cases ]

JEE Main 2022 Solution View → 112

Let A = ( cases 4 & - 2 α & β cases ) . If A ^ 2 + + 18I = O , then det (A) is equal to _______.

JEE Main 2022 Solution View → 113

Consider a matrix A = [ cases α & β & γ α ^ 2 & β ^ 2 & γ ^ 2 β + γ & γ + α & α + β cases ] , where α, β, γ are three distinct natural numbers. If det (adj ( adj (adj(adj A))) (α

JEE Main 2022 Solution View → 114

Let A = ( cases 1 & 2 - 2 & - 5 cases ) . Let α, β ∈ ℝ be such that α A ^ 2 + = 2I . Then α + β is equal to

JEE Main 2022 Solution View → 115

Let S be the set containing all 3 × 3 matrices with entries from \ - 1, 0, 1\ . The total number of matrices A ∈ S such that the sum of all the diagonal elements of A ^ T A is 6

JEE Main 2022 Solution View → 116

Let A = [ array ll 1 1 1 array ] and B = [ cases 9 ^ 2 & - 10 ^ 2 & 11 ^ 2 12 ^ 2 & 13 ^ 2 & - 14 ^ 2 - 15 ^ 2 & 16 ^ 2 & 17 ^ 2 cases ] , then the value of A ^ ' BA is;

JEE Main 2022 Solution View → 117

The number of matrices A = [ cases a & b c & d cases ] , where a, b, c, d ∈ \ - 1, 0, 1, 2, 3, … … , 10\ , such that A = A ^ - 1 , is ______.

JEE Main 2022 Solution View → 118

Let A be a 2 × 2 matrix with det(A)=-1 and det((A+I)(Adj(A)+I))=4 . Then the sum of the diagonal elements of A can be:

JEE Main 2022 Solution View → 119

Let A = [ cases 1 & a & a 0 & 1 & b 0 & 0 & 1 cases ], a, b ∈ ℝ . If for some n ∈ N, A ^ n = [ cases 1 & 48 & 2160 0 & 1 & 96 0 & 0 & 1 cases ] then n + a + b is equal to _______.

JEE Main 2022 Solution View → 120

Let A = [ cases 2 & - 1 & - 1 1 & 0 & - 1 1 & - 1 & 0 cases ] and B = A - I. If ω = 3 i - 1 2 , then the number of elements in the set \ n ∈ \ 1, 2, … , 100\ : A ^ n + ( ) ^ n = A

JEE Main 2022 Solution View → 121

Let A = ( cases 2 & - 1 0 & 2 cases ) . If B = I - C1 5 (adj A) + C2 5 ( adj A ) ^ 2 - . . . - C5 5 ( adjA ) ^ 5 , then the sum of all elements of the matrix B is:

JEE Main 2022 Solution View → 122

Let M = [ cases 0 & - α α & 0 cases ] , where α is a non-zero real number and N = ∑ _ k = 1 ^ 49 M ^ 2k . If (I - M ^ 2 )N = - 2I , then the positive integral value of α is ______.

JEE Main 2022 Solution View → 123

The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to

JEE Main 2022 Solution View → 124

Let A = [ a _ ij ] be a square matrix of order 3 such that a _ ij = 2 ^ j - i , for all i, j = 1, 2, 3 . Then, the matrix A ^ 2 + A ^ 3 + … + A ^ 10 is equal to

JEE Main 2022 Solution View → 125

Let A = ( cases 1 + i & 1 - i & 0 cases ) where i = - 1 . Then, the number of elements in the set \ n ∈ 1, 2, … . , 100 : A ^ n = A\ is

JEE Main 2022 Solution View → 126

Let A be a matrix of order 3 × 3 and det(A) = 2 . Then det(det ( A ) adj (5 adj ( A ^ 3 ))) is equal to _____.

JEE Main 2022 Solution View → 127

Let A and B be two 3 × 3 matrices such that AB = I and |A| = (1)/(8) then |adj(Badj(2A))| is equal to

JEE Main 2022 Solution View → 128

Let A be a matrix of order 2 × 2 , whose entries are from the set \ 0, 1, 2, 3, 4, 5\ . If the sum of all the entries of A is a prime number p, 2 < p < 8 , then the number of such

JEE Main 2022 Solution View → 129

The positive value of the determinant of the matrix A , whose Adj(Adj(A)) = [ cases 14 & 28 & - 14 - 14 & 14 & 28 28 & - 14 & 14 cases ] , is ______.

JEE Main 2022 Solution View → 130

Let X = [ cases 0 & 1 & 0 0 & 0 & 1 0 & 0 & 0 cases ], Y = + + γ X ^ 2 and Z = α ^ 2 I - α + ( β ^ 2 - αγ) X ^ 2 , α, β, γ ∈ ℝ . If Y ^ - 1 = [ cases (1)/(5) & (- 2)/(5) & (1)/(5)

JEE Main 2022 Solution View → 131

Let A be a 3 × 3 invertible matrix. If |adj(24A)| =adj (3 adj (2A)) | , then |A| ^ 2 is equal to

JEE Main 2022 Solution View → 132

Let A = ( cases 2 & - 2 1 & - 1 cases ) and B = ( cases - 1 & 2 - 1 & 2 cases ) . Then the number of elements in the set (n, m): n, m ∈ \ 1, 2, … … . 10\ and n A ^ n + m B ^ m = I

JEE Main 2022 Solution View → 133

Let A = [ cases 0 & - 2 2 & 0 cases ] . If M and N are two matrices given by M = ∑ _ k = 1 ^ 10 A ^ 2k and N = ∑ _ k = 1 ^ 10 A ^ 2k - 1 then M N ^ 2 is

JEE Main 2022 Solution View → 134

Let A be a 3 × 3 matrix having entries from the set \ - 1, 0, 1\ . The number of all such matrices A having sum of all the entries equal to 5 , is _____

JEE Main 2022 Solution View → 135

Let S = \ ( cases - 1 & a 0 & b cases ); a, b ∈ \ 1, 2, 3, … 100\ \ and let T _ n = \ A ∈ S: A ^ n(n + 1) = I\ . Then the number of elements in ∩ _ n = 1 ^ 100 T _ n is _____.

JEE Main 2022 Solution View → 136

Let S = n : 1 ⩽ n ⩽ 50 and n is odd . Let a ∈ S and A = [ cases 1 & 0 & a - 1 & 1 & 0 - a & 0 & 1 cases ] . If Σ _ a ∈ S det (adj A) = 100λ , then λ is equal to

JEE Main 2022 Solution View → 137

For any 3 × 3 matrix M , let | M | denote the determinant of M . Let E = [ cases 1 & 2 & 3 2 & 3 & 4 8 & 13 & 18 cases ], P = [ cases 1 & 0 & 0 0 & 0 & 1 0 & 1 & 0 cases ] and F =

JEE Advanced 2021 Solution View → 138

For any 3 × 3 matrix M , let | M | denote the determinant of M . Let I be the 3 × 3 identity matrix. Let E and F be two 3 × 3 matrices such that ( I - EF ) is invertible. If G = (

JEE Advanced 2021 Solution View → 139

The number of elements in the set A = [ cases a & b 0 & d cases ]: a, b, d ∈ - 1, 0, 1 and ( I - A ) ^ 3 = I - A ^ 3 , where I is 2 × 2 identity matrix, is .

JEE Main 2021 Solution View → 140

If the matrix A = [ cases 0 & 2 K & - 1 cases ] satisfies A( A ^ 3 + 3I) = 2I, then the value of K is

JEE Main 2021 Solution View → 141

Let A = [ cases 1 & 0 & 0 0 & 1 & 1 1 & 0 & 0 cases ] . Then A ^ 2025 - A ^ 2020 is equal to

JEE Main 2021 Solution View → 142

Let A be a 3 × 3 real matrix. If det ( 2 Adj ( 2 Adj ( Adj ( 2A ) ) ) ) = 2 ^ 41 , then the value of det ( A ^ 2 ) equals ______.

JEE Main 2021 Solution View → 143

If A = [ cases 1 5 & 2 5 - 2 5 & 1 5 cases ], B = [ cases 1 & 0 i & 1 cases ], i = - 1 , and Q = A ^ T BA , then the inverse of the matrix A Q ^ 2021 A ^ T is equal to:

JEE Main 2021 Solution View → 144

Let A and B be two 3 × 3 real matrices such that ( A ^ 2 - B ^ 2 ) is invertible matrix. If A ^ 5 = B ^ 5 and A ^ 3 B ^ 2 = A ^ 2 B ^ 3 , then the value of the determinant of the

JEE Main 2021 Solution View → 145

If A = [ cases 1 & 1 & 1 0 & 1 & 1 0 & 0 & 1 cases ] and M = A + A ^ 2 + A ^ 3 + … + A ^ 20 , then the sum of all the elements of the matrix M is equal to _______.

JEE Main 2021 Solution View → 146

Let A = [ cases 1 & 2 - 1 & 4 cases ] . If A ^ - 1 = + , α, β ∈ R, I is a 2 × 2 identity matrix, then 4(α - β) is equal to :

JEE Main 2021 Solution View → 147

If P = [ cases 1 & 0 (1)/(2) & 1 cases ], then P ^ 50 is:

JEE Main 2021 Solution View → 148

Let M = \ A = [ cases a & b c & d cases ]: a, b, c, d ∈ (± 3, ± 2, ± 1, 0)\ . Define f: M → Z, as f(A) = det (A), for all A ∈ M where Z is set of all integers. Then the number of

JEE Main 2021 Solution View → 149

Let S = \ n ∈ N, ( cases 0 & i 1 & 0 cases ) ^ n ( cases a & b c & d cases ) = ( cases a & b c & d cases ) ∀ a, b, c, d ∈ R\ , where i = - 1 . Then the number of 2 - digit numbers

JEE Main 2021 Solution View → 150

Let A = [ a _ ij ] be a real matrix of order 3 × 3, such that a _ i1 + a _ i2 + a _ i3 = 1, for i = 1, 2, 3 . Then, the sum of all the entries of the matrix A ^ 3 is equal to:

JEE Main 2021 Solution View → 151

Let A = [ cases 0 & 1 & 0 1 & 0 & 0 0 & 0 & 1 cases ] . Then the number of 3 × 3 matrices B with entries from the set 1, 2, 3, 4, 5 and satisfying AB = BA is ________.

JEE Main 2021 Solution View → 152

Let A = \ a _ ij \ be a 3 × 3 matrix, where a _ ij = \ array ll (- 1) ^ j - i ifi j array ) then det(3 Adj (2 A ^ - 1 )) is equal to ________.

JEE Main 2021 Solution View → 153

Let A = [ cases 2 & 3 a & 0 cases ], a ∈ R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det (Q) = 9 , then the modulus of the sum of all

JEE Main 2021 Solution View → 154

Let A = [ array ll 1 - 1 0 0 & 1 & - 1 0 & 0 & 1 array ] and B = 7 A ^ 20 - 20 A ^ 7 + 2I , where I is an identity matrix of order 3 × 3 . If B = [ b _ ij ] , then b _ 13 is equal

JEE Main 2021 Solution View → 155

Let I be an identity matrix of order 2 × 2 and P = [ cases 2 & - 1 5 & - 3 cases ] . Then the value of n ∈ N for which P ^ n = 5I - 8P is equal to ___ .

JEE Main 2021 Solution View → 156

Let A + 2B = [ cases 1 & 2 & 0 6 & - 3 & 3 - 5 & 3 & 1 cases ] and 2A - B = [ cases 2 & - 1 & 5 2 & - 1 & 6 0 & 1 & 2 cases ] . If Tr(A) denotes the sum of all diagonal elements

JEE Main 2021 Solution View → 157

Let A = [ cases a & b c & d cases ] and B = [ array ll α β array ] ≠ [ array ll 0 0 array ] such that AB = B and a + d =2021, then the value of ad - bc is equal to ______ .

JEE Main 2021 Solution View → 158

If A = [ cases 0 & sinα sinα & 0 cases ] and det( A ^ 2 - (1)/(2)I) = 0, then a possible value of α is

JEE Main 2021 Solution View → 159

If A = [ cases 2 & 3 0 & - 1 cases ], then the value of det ( A ^ 4 ) + det ( A ^ 10 - ( Adj ( 2A ) ) ^ 10 ) is equal to ________.

JEE Main 2021 Solution View → 160

Let A = [ array ll a _ 1 a _ 2 array ] and B = [ array ll b _ 1 b _ 2 array ] be two 2 × 1 matrices with real entries such that A = XB, where X = 1 3 [ cases 1 & - 1 1 & k cases

JEE Main 2021 Solution View → 161

Let A = [ cases i & - i - i & i cases ], i = - 1 . Then, the system of linear equations A ^ 8 [ array ll x y array ] = [ array ll 8 64 array ] has :

JEE Main 2021 Solution View → 162

Let P = [ cases - 30 & 20 & 56 90 & 140 & 112 120 & 60 & 14 cases ] and A = [ cases 2 & 7 & ω ^ 2 - 1 & - ω & 1 0 & - ω & - ω + 1 cases ] where ω = - 1 + i 3 2 , and I _ 3 be the

JEE Main 2021 Solution View → 163

The total number of 3 × 3 matrices A having enteries from the set (0, 1, 2, 3) such that the sum of all the diagonal entries of A A ^ T is 9 , is equal to

JEE Main 2021 Solution View → 164

If the matrix A = [ cases 1 & 0 & 0 0 & 2 & 0 3 & 0 & - 1 cases ] satisfies the equation A ^ 20 + α A ^ 19 + = [ cases 1 & 0 & 0 0 & 4 & 0 0 & 0 & 1 cases ] for some real numbers

JEE Main 2021 Solution View → 165

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A ^ 2 is 1, then the possible number of such matrices is:

JEE Main 2021 Solution View → 166

If for the matrix, A = [ cases 1 & - α α & β cases ], A A ^ T = I _ 2 , then the value of α ^ 4 + β ^ 4 is :

JEE Main 2021 Solution View → 167

If A = [ cases 0 & - tan((θ)/(2)) tan((θ)/(2)) & 0 cases ] and ( I _ 2 + A) ( I _ 2 - A) ^ - 1 = [ cases a & - b b & a cases ], then 13( a ^ 2 + b ^ 2 ) is equal to _____ .

JEE Main 2021 Solution View → 168

Let A = [ cases x & y & z y & z & x z & x & y cases ], where x, y and z are real numbers such that x + y + z > 0 and xyz = 2 . If A ^ 2 = I _ 3 , then the value of x ^ 3 + y ^ 3 +

JEE Main 2021 Solution View → 169

Let P = [ cases 3 & - 1 & - 2 2 & 0 & α 3 & - 5 & 0 cases ], where α ∈ R . Suppose Q = [ q _ ij ] is a matrix satisfying PQ = k I _ 3 for some non-zero k ∈ R . If q _ 23 =

JEE Main 2021 Solution View → 170

Let M be any 3 × 3 matrix with entries from the set \ 0, 1, 2\ . The maximum number of such matrices, for which the sum of diagonal elements of M ^ T M is seven, is______.

JEE Main 2021 Solution View → 171

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 × 2 matrix such that the trace of A is 3 and the trace of A ^ 3 is - 18 then the value

JEE Advanced 2020 Solution View → 172

Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity matrix. M ^ - 1 = adj(adjM) , then which of the following statements is/are ALWAYS TRUE?

JEE Advanced 2020 Solution View → 173

Let θ = (π)/(5) and A = [ cases cos θ & sin θ - sin θ & cos θ cases ] . If B = A + A ^ 4 , then det (B) :

JEE Main 2020 Solution View → 174

If A = [ cases cosθ & isinθ isinθ & cosθ cases ], (θ = (π)/(24)) and A ^ 5 = [ cases a & b c & d cases ], where i = - 1 , then which one of the following is not true?

JEE Main 2020 Solution View → 175

Let A be a 3 × 3 matrix such that adj A = [ cases 2 & - 1 & 1 - 1 & 0 & 2 1 & - 2 & - 1 cases ] and B = adj (adjA) . If | A | = λ and | ( B ^ - 1 ) ^ ⊤ | = μ , then the ordered

JEE Main 2020 Solution View → 176

Let A = [ cases x & 1 1 & 0 cases ], xεR and A ^ 4 = [ a _ ij ] . If a _ 11 = 109, then a _ 22 is equal to_____________.

JEE Main 2020 Solution View → 177

Let A = \ X = (x, y, z) ^ T : PX = 0and x ^ 2 + y ^ 2 + z ^ 2 = 1\ where P = [ cases 1 & 2 & 1 - 2 & 3 & - 4 1 & 9 & - 1 cases ] then the set A

JEE Main 2020 Solution View → 178

Let a, b, c ∈ R be all non-zero and satisfies a ^ 3 + b ^ 3 + c ^ 3 = 2 . If the matrix A = [ cases a & b & c b & c & a c & a & b cases ] satisfies A ^ T A = I, then a value of

JEE Main 2020 Solution View → 179

Let A be a 2 × 2 real matrix with entries from \ 0, 1\ and |A| ≠ 0 . Consider the following two statements; (P) If A ≠ l _ 2 , then |A| = - 1 (Q) If |A| = 1 , then tr(A) = 2 Where

JEE Main 2020 Solution View → 180

If A = [ cases 1 & 1 & 2 1 & 3 & 4 1 & - 1 & 3 cases ], B = adjA and C = 3A, then (|adjB|)/(|C|) is equal to

JEE Main 2020 Solution View → 181

If A = ( cases 2 & 2 9 & 4 cases ) and I = ( cases 1 & 0 0 & 1 cases ), then 10 A ^ - 1 , is equal to.

JEE Main 2020 Solution View → 182

The number of all 3 × 3 matrices A, with entries from the set \ - 1, 0, 1\ such that the sum of the diagonal elements of A A ^ T is 3, is ___________.

JEE Main 2020 Solution View → 183

Let α be a root of the equation x ^ 2 + x + 1 = 0 and the matrix A = 1 3 [ cases 1 & 1 & 1 1 & α & α ^ 2 1 & α ^ 2 & α ^ 4 cases ], then the matrix A ^ 31 is equal to

JEE Main 2020 Solution View → 184

Let P _ 1 = I = [ cases 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 cases ], P _ 2 = [ cases 1 & 0 & 0 0 & 0 & 1 0 & 1 & 0 cases ], P _ 3 = [ cases 0 & 1 & 0 1 & 0 & 0 0 & 0 & 1 cases ], P _ 4

JEE Advanced 2019 Solution View → 185

Let M = [ cases ^ 4 ⁡ θ & - 1 - ^ 2 ⁡ θ 1 + ^ 2 ⁡ θ & ^ 4 ⁡ θ cases ] = + β M ^ - 1 , where α = α(θ) and β = β(θ) are real number, and I is the 2 × 2 identity matrix. If α ^ * is

JEE Advanced 2019 Solution View → 186

Let M = [ cases 0 & 1 & a 1 & 2 & 3 3 & b & 1 cases ] and adjM = [ cases - 1 & 1 & - 1 8 & - 6 & 2 - 5 & 3 & - 1 cases ] where a and b are real numbers. Which of the following

JEE Advanced 2019 Solution View → 187

If B = [ cases 5 & 2α & 1 0 & 2 & 1 α & 3 & - 1 cases ] is the inverse of a 3 × 3 matix A, then the sum of all values of α for which det(A) + 1 = 0, is:

JEE Main 2019 Solution View → 188

If A is a symmetric matrix and B is skew- symmetric matrix such that A + B = [ cases 2 & 3 5 & - 1 cases ] , then AB is equal to:

JEE Main 2019 Solution View → 189

The total number of matrices A = ( cases 0 & 2y & 1 2x & y & - 1 2x & - y & 1 cases ), (x, y ∈ R, x ≠ y) for which A ^ T A = 3 I _ 3 is:

JEE Main 2019 Solution View → 190

If [ cases 1 & 1 0 & 1 cases ][ cases 1 & 2 0 & 1 cases ][ cases 1 & 3 0 & 1 cases ] … . [ cases 1 & n - 1 0 & 1 cases ] = [ cases 1 & 78 0 & 1 cases ], then the inverse of [

JEE Main 2019 Solution View → 191

Let A = [ cases cosα & - sinα sinα & cosα cases ], (a ∈ R) such that A ^ 32 = [ cases 0 & - 1 1 & 0 cases ] . Then, a value of α is:

JEE Main 2019 Solution View → 192

Let P = [ cases 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 cases ] and Q = [ q _ ij ] be two 3 × 3 matrices such that Q - P ^ 5 = I _ 3 . Then q _ 21 + q _ 31 q _ 32 is equal to :

JEE Main 2019 Solution View → 193

Let A=( array ccc 0 & 2 q & r p & q & -r p & -q & r array ) . If AA^ T =I_ 3 , then |p| is:

JEE Main 2019 Solution View → 194

If A = [ cases e ^ t & e ^ - t cost & e ^ - t sin ⁡t e ^ t & - e ^ - t cos ⁡ t - e ^ - t sin ⁡ t & - e ^ - t sin ⁡ t + e ^ - t cos ⁡ t e ^ t & 2e ^ - t sin ⁡ t & - 2 e ^ - t cos ⁡

JEE Main 2019 Solution View → 195

If A = [ cases cosθ & - sinθ sinθ & cosθ cases ] , then the matrix A ^ - 50 when θ = (π)/(12), is equal to:

JEE Main 2019 Solution View → 196

Let A = [ cases 1 & 0 & 0 1 & 1 & 0 1 & 1 & 1 cases ] and B = A ^ 20 . Then the sum of the elements of the first column of B is

JEE Main 2018 Solution View → 197

Suppose A is any 3 × 3 non-singular matrix and (A-3 I)(A-5 I)=O , where I=I_3 and O=O_3 . If α A+ β A^ -1 =4 I , then α+β is equal to

JEE Main 2018 Solution View → 198

The number of 3 × 3 matrices M with entries from 0,1, 2 , such that the sum of the diagonal elements of M ^ T M is 5 , are

JEE Advanced 2017 Solution View → 199

Let P = [ cases 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 cases ] and I be the identity matrix of order 3 . If Q = [ q _ ij ] is a matrix such that P ^ 50 - Q = I, then the value of q _ 31 +

JEE Advanced 2016 Solution View → 200

Let P = [ cases 3 & - 1 & - 2 2 & 0 & α 3 & - 5 & 0 cases ] , where α ∈ R, Suppose Q = [ q _ ij ] is a matrix such that PQ = kI , where k ∈ R, k ≠ 0 and I is the identity matrix

JEE Advanced 2016 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Matrices in other exams

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