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Matrices — JEE Main & Advanced Mathematics PYQs

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

506 questionsMathematicsSolutions on every page
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 M²⁶ = bmatrix p & q r & s bmatrix and _ k=1 ²⁶ M^k = bmatrix a & b c & d

JEE Advanced 2026 Solution View → 3

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

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 number

JEE Advanced 2026 Solution View → 5

Let A = bmatrix & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 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 = A⁹⁹ - I , then the value of b₃₁ - b₂₁ b₃₂ is :

JEE Main 2026 Solution View → 7

Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + (adj(adj(A))) + (adj(A)(adj(adj(A)))) = bmatrix 2 & -2 & 2 -2 & 0 & -1 0 & 0 & -1 bmatrix for some , R . Then

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 pmatr

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 bmat

JEE Main 2026 Solution View → 10

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

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 of the diago

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( adj A)⁻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 s

JEE Main 2026 Solution View → 14

Let A = bmatrix 1 & 2 1 & bmatrix and B = bmatrix 3 & 3 & 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 = bmatrix 13

JEE Main 2026 Solution View → 15

Let A= [ array ll 3 & -4 1 & -1 array ] and B be two matrices such that A¹⁰⁰=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 x₁ x₂ array ]= [ array c 12 -6

JEE Main 2026 Solution View → 17

Let f(x)= 7 x¹⁰+9 x⁸ (1+x²+2 x⁹ )² d x, x>0, _ x 0 f(x)=0 and f(1)= 1 4 . If A = [ array ccc 0 & 0 & 1 1 4 & f^ (1) & 1 ² & 4 & 1 array ] and B = adj ( adj A ) be such that | B |=8

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 )=2¹⁰ . 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 ] , th

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 a

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 fo

JEE Main 2026 Solution View → 26

For some , R , let A= [ array ll & 2 1 & 2 array ] and B= [ array ll 1 & 1 1 & array ] be such that A²-4 A+2 I=B²-3 B+I=O . Then ( det ( adj (A³-B³ ) ) )² is equal to _ _ _ _ .

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 int

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

JEE Advanced 2025 Solution View → 29

Let 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 equal

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 & 0 & - 0 & 1 & 0 & 0 & array ] . If for some (0, ) , 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 & 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^ 3^ 5^ , , N then + + 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= A^2+ A+ I , where , and are real constants,

JEE Main 2025 Solution View → 38

Let A= [ array cc & -1 6 & array ], 0 , such that det (A)=0 and + =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 det ((a+1)

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 + 2 , , Z , then + 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 _

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 & - & array ], 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 , n

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 ] M : A =-

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 ]= [ arr

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 the v

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 n . Then 4 ~m +2 n is equal to _______

JEE Main 2025 Solution View → 50

Let and be the distinct roots of the equation x^2+x-1=0 . Consider the set T= 1, , . 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_ 1 j +a_ 2 j +

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+ C^2+ I=O , then 2 - 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 A¹³ 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 0 and A= [ array rrr & & 3 & & - & & 2 array ] . If B= [ array rrr 3 & -9 & 3 - & 7 & -2 -2 & 5 & -2 array ] is the matrix of cofactors of the elements of A , then det (A B) is

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= A+ I , where I is an identity matrix of order 2 2 ,

JEE Main 2024 Solution View → 60

Let (0, ) and A= [ array lll 1 & 2 & 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 − 2 M 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 A X = λ X holds for some non-ze

JEE Main 2024 Solution View → 63

If A = 2 1 − 1 2 , B 1 0 1 1 , C = A B 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 a d j a d j . ... a d j A ⏟ 2024 − times , then the remainder when n is divided by 9 is equal to __________.

JEE Main 2024 Solution View → 65

Let R = x 0 0 0 y 0 0 0 z be a non-zero 3 × 3 matrix, where x sin θ = y sin θ + 2 π 3 = z sin θ + 4 π 3 ≠ 0 , θ ∈ ( 0 , 2 π ) . For a square matrix M , let Trace M denote the sum o

JEE Main 2024 Solution View → 66

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

JEE Main 2024 Solution View → 67

Let A = 1 0 0 0 α β 0 β α and | 2 A | 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 matri

JEE Main 2024 Solution View → 70

Let A = 2 0 1 1 1 0 1 0 1 , B = B 1 B 2 B 3 , where B 1 , B 2 , B 3 are column matrices, and AB 1 = 1 0 0 , AB 2 = 2 3 0 , AB 3 = 3 2 1 If α = | B | and β is the sum of all the dia

JEE Main 2024 Solution View → 71

Consider the matrix f x = cos x - sin x 0 sin x cos x 0 0 0 1 . Given below are two statements : Statement I: f ( - x ) is the inverse of the matrix f ( x ) . Statement II: f ( x )

JEE Main 2024 Solution View → 72

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

JEE Advanced 2023 Solution View → 73

Let R = a 3 b c 2 d 0 5 0 : 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 4 m + n = 22 and 17 m + 4 n = 93 . If d e t n a d j a d j m A = 3 a 5 b 6 c , then a + b + c is

JEE Main 2023 Solution View → 75

Let for A = 1 2 3 α 3 1 1 1 2 , A = 2 . If | 2 adj ( 2 adj ( 2 A ) ) | = 32 n , then 3 n + 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 = 1 3 α 1 2 3 α α 4 , α > 2 be the adjoint of a matrix A and A = 2 . Then α - 2 α α B α - 2 α α is equal to

JEE Main 2023 Solution View → 78

Let A = 1 1 51 0 1 . If B = 1 2 - 1 - 1 A - 1 - 2 1 1 , then the sum of all the elements of the matrix ∑ n = 1 50 B n is equal to

JEE Main 2023 Solution View → 79

Let A = 0 1 2 a 0 3 1 c 0 , 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 equal to ____

JEE Main 2023 Solution View → 80

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

JEE Main 2023 Solution View → 81

If A = 1 5 ! 6 ! 7 ! 5 ! 6 ! 7 ! 6 ! 7 ! 8 ! 7 ! 8 ! 9 ! , then adj adj 2 A is equal to

JEE Main 2023 Solution View → 82

If A is a 3 × 3 matrix and A = 2 , then 3 adj 3 A A 2 is equal to

JEE Main 2023 Solution View → 83

If A = 1 5 λ 10 , A - 1 = α A + β I and α + β = - 2 , then 4 α 2 + β 2 + λ 2 is equal to :

JEE Main 2023 Solution View → 84

Let 2 1 0 1 2 - 1 0 - 1 2 . If a d j ( a d j a d j 2 A ) = ( 16 ) n , then n is equal to

JEE Main 2023 Solution View → 85

Let P = 3 2 1 2 - 1 2 3 2 , A = 1 1 0 1 and Q = P A P T . If P T Q 2007 P = a b c d then 2 a + b - 3 c - 4 d is equal to

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 = γ l - 29 P and P α - P β = δ l

JEE Main 2023 Solution View → 87

Let A = a i j 2 × 2 , where a ≠ i j 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 1 3 - 3 1 then,

JEE Main 2023 Solution View → 89

Let A = a i ^ j ^ · a i j ∈ 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 = 1 0 0 0 4 - 1 0 12 - 3 . 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 = a P + ( a - 1 ) I , where a > 1 , then

JEE Main 2023 Solution View → 93

Let A = m n p q , 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 e t e - t sin t - 2 cos t e - t - 2 sin t - cos t e t e - t 2 sin t + cos t e - t sin t - 2 cos t e t e - t cos t

JEE Main 2023 Solution View → 95

Let A be a symmetric matrix such that A = 2 and 2 1 3 3 2 A = 1 2 α β If the sum of the diagonal elements of A is s , then β s α 2 is equal to _________.

JEE Main 2023 Solution View → 96

Let α and β be real numbers. Consider a 3 × 3 matrix A such that A 2 = 3 A + α I . If A 4 = 21 A + β I , 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 S 1 A 13 B 26 - B 26 A 13 is symmetric S 2 A 26 C 13 - C 13 A

JEE Main 2023 Solution View → 98

Let A = 1 10 3 10 - 3 10 1 10 and B = 1 - i 0 1 , 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 = 1 log x y log x z log y x 2 log y z log z x log z y 3 . 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 a d j a d j a d j . A = 12 4 . Then A - 1 a d j A 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 = β 0 1 2 1 - 2 3 1 - 2 . If A 7 - β - 1 A 6 - β A 5 is a singular matrix, then the value of 9 β is _____ .

JEE Advanced 2022 Solution View → 104

If M = 5 2 3 2 - 3 2 - 1 2 , 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 - 1 2 1 - 1 by a single elementary row operation?

JEE Main 2022 Solution View → 106

Let x = 1 1 1 and A = - 1 2 3 0 1 6 0 0 - 1 . 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 A B 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 = 0 1 0 1 0 0 0 0 1 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 to

JEE Main 2022 Solution View → 111

Let A = 1 - 1 2 α and B = β 1 1 0 , α , β ∈ R . Let α 1 be the value of α which satisfies A + B 2 = A 2 + 2 2 2 2 and α 2 be the value of &

JEE Main 2022 Solution View → 112

Let A = 4 - 2 α β . If A 2 + γ A + 18 I = O , then det A is equal to _______.

JEE Main 2022 Solution View → 113

Consider a matrix A = α β γ α 2 β 2 γ 2 β + γ γ + α α + β , where α , β , γ are three distinct natural nu

JEE Main 2022 Solution View → 114

Let A = 1 2 - 2 - 5 . Let α , β ∈ ℝ be such that α A 2 + β A = 2 I . 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

JEE Main 2022 Solution View → 116

Let A = 1 1 1 and B = 9 2 - 10 2 11 2 12 2 13 2 - 14 2 - 15 2 16 2 17 2 , then the value of A ' B A is;

JEE Main 2022 Solution View → 117

The number of matrices A = a b c d , 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 = 1 a a 0 1 b 0 0 1 , a , b ∈ ℝ . If for some n ∈ N , A n = 1 48 2160 0 1 96 0 0 1 then n + a + b is equal to _______.

JEE Main 2022 Solution View → 120

Let A = 2 - 1 - 1 1 0 - 1 1 - 1 0 and B = A - I . If ω = 3 i - 1 2 , then the number of elements in the set n ∈ 1 , 2 , … , 100 : A n + ω B n = A + B is equal

JEE Main 2022 Solution View →
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