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NDA Matrices PYQs with Solutions

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

153 questionsMathematics2010–2026Answers + solutions

About Matrices PYQs

Matrices has 153 previous year questions in the Quantrex Academy NDA Mathematics bank. The 153 questions in this list come from NDA (153), spanning 2010 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: 4
  • 2025: 10
  • 2024: 12
  • 2023: 9
  • 2022: 10
  • 2021: 8
  • 2020: 5
  • 2019: 6
  • 2018: 11
  • 2017: 14
  • 2016: 7
  • 2015: 11

Matrices questions with solutions

1

Consider the following statements : I. If n× n(n > 1) matrix is symmetric, then its inverse is also a symmetric matrix. II. If n× n(n > 1) matrix is singular, then its adjoint is

NDA 2026 Solution View → 2

If M is a square matrix such that M^3=M , then how many values of |M| are possible ?

NDA 2026 Solution View → 3

If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is |M_1|+|M_2|+|M_3|+…+|M_ 50 | equal to ?

NDA 2026 Solution View → 4

If M^ T is the transpose of a 2×2 matrix M , then which of the following is/are correct ? I. |M+M^ T |=|M|+|M^ T | if M is symmetric. II. |M+M^ T |=0 if M is anti-symmetric.

NDA 2026 Solution View → 5

Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 = A^ -1 B^ -1 II. (BA)(AB)^ -1 = I , where I is the identity matrix III. (AB)^T = A^T B^T How many

NDA 2025 Solution View → 6

For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is [adj\, A]^ -1 equal to?

NDA 2025 Solution View → 7

Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29 65 & 17 & 48 pmatrix : Statement-I: The inverse of M does not exist. Statement-II: M is

NDA 2025 Solution View → 8

If [x \ 1 \ 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45] , then which one of the following is a value of x ?

NDA 2025 Solution View → 9

If A = pmatrix 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 pmatrix , then what is A^2 - 4A equal to?

NDA 2025 Solution View → 10

If A = pmatrix y & z & x z & x & y x & y & z pmatrix where x , y , z are integers, is an orthogonal matrix, then what is the value of x^2 + y^2 + z^2 ?

NDA 2025 Solution View → 11

If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an orthogonal matrix, then what is A^2 equal to?

NDA 2025 Solution View → 12

For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is the value of the determinant of the matrix A^4 ?

NDA 2025 Solution View → 13

What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2 pmatrix ?

NDA 2025 Solution View → 14

If f(θ) = pmatrix θ & θ - θ & θ pmatrix , then what is \ f(π)\ ^2 equal to?

NDA 2025 Solution View → 15

Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order 3 × 2 . Which of the following statements are correct? A. (ZY) X is defined and is a

NDA 2024 Solution View → 16

Let A and B be two square matrices of same order. If A B is a null matrix, then which one of the following is correct?

NDA 2024 Solution View → 17

Consider the following in respect of the matrices P=[ array ccc 0 & c & -b -c & 0 & a b & -a & 0 array ] and Q=[ array ccc a^2 & a b & a c a b & b^2 & b c a c & b c & c^2 array ]

NDA 2024 Solution View → 18

If P is a skew-symmetric matrix of order 3 , then what is (P) equal to?

NDA 2024 Solution View → 19

Paragraph: Let A=[ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] Question: What is A(adj A) equal to?

NDA 2024 Solution View → 20

Paragraph: Let A=[ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] Question: What is A^ -1 equal to?

NDA 2024 Solution View → 21

Consider the following statements in respect of two non-singular matrices A and B of the same order n : 1. adj(AB)=(adj A)(adjB) 2. adj(AB)=adj(BA) 3. (AB) adj(AB)-|AB| I_n is a

NDA 2024 Solution View → 22

Let A and B be matrices of order 3 × 3 . If |A|= 1 2 2 and |B|=(1)/(729) , then what is the value of 2 B(adj(3 A) ?

NDA 2024 Solution View → 23

Consider the following statements in respect of a non-singular matrix A of order n : 1. A(adj A^ T )=A(adj A)^ T 2. If A^2=A , then A is identity matrix of order n 3. If A^3=A

NDA 2024 Solution View → 24

Consider the following statements in respect of a skew-symmetric matrix A of order 3: 1. All diagonal elements are zero. 2. The sum of all the diagonal elements of the matrix is

NDA 2024 Solution View → 25

What is the number of different matrices, each having 4 entries that can be formed using 1,2,3 , 4 (repetition is allowed)?

NDA 2024 Solution View → 26

If A=[ array ccc 2 θ & 2 ^2 θ-1 & 0 2 θ & 2 θ θ & 0 0 & 0 & 1 array ] , then which of the following statements is/are correct? 1. A^ -1 =adj A 2. A is skew-symmetric matrix 3. A^

NDA 2024 Solution View → 27

If A, B and C are square matrices of order 3 and (BC)=2 ( A) , then what is the value of (2 A^ -1 BC)?

NDA 2023 Solution View → 28

If A=[ array ccc 0 & 3 & 4 -3 & 0 & 5 -4 & -5 & 0 array ] , then which one of the following statements is correct?

NDA 2023 Solution View → 29

Let A be a matrix of order 3 × 3 and |A|=4 . If |2 adj(3 A)|=2^ a 3^ b , then what is the value of (α+β) ?

NDA 2023 Solution View → 30

Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (A B-B A) ? 1. Its diagonal entries are equal but non-zero 2. The sum of its

NDA 2023 Solution View → 31

Consider the following statements in respect of square matrices A, B, C each of same order n : 1. A B=A C ⇒ B=C if A is non-singular 2. If B X=C X for every column matrix X having

NDA 2023 Solution View → 32

If A=[ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] , then what is 23 A^3-19 A^2-4 A equal to?

NDA 2023 Solution View → 33

If A=[ array l 1 2 3 array ] , then what is value of (I+A A^ ) , where I is the 3 ×3 identity matrix?

NDA 2023 Solution View → 34

If A=[ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] , then which of the following statements are correct? 1. A^n will always be singular for any positive integer n . 2. A^ n

NDA 2023 Solution View → 35

If A=[ array ccc 2 & -1 & 0 -1 & 3 & 0 1 & 0 & 1 array ] , then what is the value of [adj(adj A)] ?

NDA 2023 Solution View → 36

If A=( array ccc 1 & 0 & 0 0 & θ & θ 0 & θ & - θ array ) , then which of the following are correct? 1. A+adj A is a null matrix 2. A^ -1 +adj A is a null matrix 3. A-A^ -1 is a

NDA 2022 Solution View → 37

If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2 , then which of the following are correct? 1. (Z Y) X is a square matrix having 9

NDA 2022 Solution View → 38

Paragraph: Let A=( array ccc 0 & ^2 θ & ^2 θ ^2 θ & 0 & ^2 θ ^2 θ & ^2 θ & 0 array ) and A=P+Q where P is symmetric matrix and Q is skew-symmetric matrix. Question: What is P

NDA 2022 Solution View → 39

Consider the following in respect of the matrices: A=[ array ll m & n array ], B=[ array ll -n & -m array ] and C=[ array c m -m array ] 1. C A=C B 2. A C=B C 3. C(A+B)=C A+C B

NDA 2022 Solution View → 40

If A=[ array ccc 2 θ & θ & 0 -2 θ & θ & 0 -1 & 1 & 1 array ] , then what is A(adj A) equal to? where I is the identify matrix.

NDA 2022 Solution View → 41

Let A be a non-singular matrix and B=adj A . Which of the following statements is/are correct? 1. A B=B A 2. A B is a scalar matrix 3. A B can be a null matrix Select the correct

NDA 2022 Solution View → 42

Consider the following statements in respect of square matrices A and B of same order: 1. If A B is a null matrix, then at last one of A and B is a null matrix. 2. If A B is an

NDA 2022 Solution View → 43

If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C=A+B ?

NDA 2022 Solution View → 44

Let A and B be non-singular matrices of the same order such that A B=A and B A=B . Which of the following statements is/are correct? 1. A^2=A 2. A B^2=A^2 B Select the correct

NDA 2022 Solution View → 45

Paragraph: Let A=( array ccc 0 & ^2 θ & ^2 θ ^2 θ & 0 & ^2 θ ^2 θ & ^2 θ & 0 array ) and A=P+Q where P is symmetric matrix and Q is skew-symmetric matrix. Question: What is Q

NDA 2022 Solution View → 46

If A=[ array ll 1 & a 0 & 1 array ] where a ∈ ℕ , then what is A^ 100 -A^ 50 -2 A^ 25 equal to? where I is the identity matrix.

NDA 2021 Solution View → 47

How many distinct matrices exist with all four entries taken from \ 1,2\ ?

NDA 2021 Solution View → 48

Consider the following in respect of the Matrix A=[ array lll 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 array ] 1. Inverse of A does not exist 2. A^3=A 3. 3 A=A^2 Which of the above are

NDA 2021 Solution View → 49

The inverse of a matrix A is given by [ array cc -2 & 1 (3)/(2) & - (1)/(2) array ] What is A equal to?

NDA 2021 Solution View → 50

If A and B are two matrices such that A B is of order n , then which one of the following is correct?

NDA 2021 Solution View → 51

Let A=[ array cc 0 & 2 -2 & 0 array ] and (m I+n A)^2=A where m, n are positive real numbers and I is the identity matrix. What is (m+n) equal to?

NDA 2021 Solution View → 52

How many matrices of different orders are possible with elements comprising all prime numbers less than 30 ?

NDA 2021 Solution View → 53

If A and B are square matrices of order 2 such that (A B)= (B A) , then which one of the following is correct?

NDA 2021 Solution View → 54

Consider the following in respect of a non-singular matrix of order 3 : 1. A(adj A)=(adj A) A 2. | adj A |=| A | Which of the above statements is/are correct?

NDA 2020 Solution View → 55

If A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3 , then the order of A B and B A will respectively be

NDA 2020 Solution View → 56

If matrix A=[ array cc 1-i & i -i & 1-i array ] where i= -1 , then which one of the following is correct?

NDA 2020 Solution View → 57

Let A=[ array cc x+y & y 2 x & x-y array ], B=[ array c 2 -1 array ] and C=[ array l 3 2 array ] . If A B=C , then what is the value of the determinant of the matrix A ?

NDA 2020 Solution View → 58

Let A=[ array lll a & h & g h & b & f g & f & c array ] and B=[ array l x y z array ] , then what is A B equal to?

NDA 2020 Solution View → 59

If A=( array ll 1 & 2 2 & 3 3 & 4 array ) and B=( array ll 1 & 2 2 & 1 array ) , then which one of the following is correct?

NDA 2019 Solution View → 60

If A=[ array cc 1 & -1 -1 & 1 array ] , then the expression A^3-2 A^2 is

NDA 2019 Solution View → 61

If B=[ array lll 3 & 2 & 0 2 & 4 & 0 1 & 1 & 0 array ] , then what is adjoint of B equal to?

NDA 2019 Solution View → 62

If A is an identity matrix of order 3 , then its inverse (A^ -1 )

NDA 2019 Solution View → 63

Paragraph: Let A and B be (3 × 3) matrices with A=4 and B=3 . Question: What is (3 AB^ -1 ) equal to ?

NDA 2019 Solution View → 64

If A=[ array ll 0 & 1 1 & 0 array ] , then matrix A is/an

NDA 2019 Solution View → 65

A square matrix A is called orthogonal if

NDA 2018 Solution View → 66

What is the adjoint of the matrix (-θ)- (-θ) - (-θ) (-θ) ?

NDA 2018 Solution View → 67

What should be the value of x so that the matrix ( array ll 2 & 4 -8 & x array ) does not have an inverse?

NDA 2018 Solution View → 68

If A and B are two invertible square matrices of same order, then what is (AB)^ -1 equal to?

NDA 2018 Solution View → 69

Consider the following in respect of matrices A, B and C of same order: 1. (A+B+C)^ =A^ +B^ +C^ 2. ( AB )^ = A^ B^ 3. ( ABC )^ = C^ B^ A^ Where A^ is the transpose of the matrix

NDA 2018 Solution View → 70

Consider the following in respect of matrices A and B of same order: 1. A^2-B^2=(A+B)(A-B) 2. (A-I)(I+A)=0 ⇔ A^2=I Where I is the identity matrix and O is the null matrix. Which

NDA 2018 Solution View → 71

Let matrix B be the adjoint of a square matrix A,I be the identity matrix of same order as A . If k(≠ 0) is the determinant of the matrix A , then what is AB equal to?

NDA 2018 Solution View → 72

If A is a 2 × 3 matrix and A B is a 2 × 5 matrix, then B must be a

NDA 2018 Solution View → 73

What is the inverse of the matrix A=( array ccc θ & θ & 0 - θ & θ & 0 0 & 0 & 1 array )

NDA 2018 Solution View → 74

If A=[ array ll 1 & 2 2 & 3 array ] and A^2-k A-I_2=O , where I_2 is the 2 × 2 identity matrix, then what is the value of k ?

NDA 2018 Solution View → 75

For a square matrix A , which of the following properties hold? 1. (A^ -1 )^ -1 =A 2. det(A^ -1 )= 1 det ~A 3. (λ A)^ -1 λ ~A^ -1 where λ is a scalar Select the correct answer

NDA 2018 Solution View → 76

The matrix A has x rows and x+5 columns. The matrix B has y rows and 11-y columns. Both AB and BA exist. What are the values of x and y respectively?

NDA 2017 Solution View → 77

If A=[ array cc 4 i-6 & 10 i 14 i & 6+4 i array ] and k= 1 2 i^ where i= -1 , then kA is equal to

NDA 2017 Solution View → 78

If A is a square matrix, then the value of adj A^T-(adj A)^T is equal to

NDA 2017 Solution View → 79

If a, b, c are non-zero real numbers, then the inverse of the matrix A=[ array lll a & 0 & 0 0 & b & 0 0 & 0 & c array ] is equal to

NDA 2017 Solution View → 80

The adjoint of the matrix A=[ array lll 1 & 0 & 2 2 & 1 & 0 0 & 3 & 1 array ] is

NDA 2017 Solution View → 81

If A=( array cc -2 & 2 2 & -2 array ) , then which one of the following is correct?

NDA 2017 Solution View → 82

If A=[ array cc α & 2 2 & α array ] and (A^3)=125 , then α is equal to

NDA 2017 Solution View → 83

If B is a non-singular matrix and A is a square matrix, then the value of (B^ -1 A B) is equal to

NDA 2017 Solution View → 84

If A=[ array cc α & α - α & α array ] then what is AA ^T equal to (where A^ T is the transpose of A ) ?

NDA 2017 Solution View → 85

A=[ array cc x+y & y x & x-y array ], B=[ array l 3 -2 array ] and C=[ array l 4 -2 array ] . If A B=C , then what is A^2 equal to?

NDA 2017 Solution View → 86

If A=[ array ll θ & θ - θ & θ array ] , then what is A^3 equal to?

NDA 2017 Solution View → 87

Consider the set A of all matrices of order 3 × 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A

NDA 2017 Solution View → 88

If A=[ array ll 0 & 1 1 & 0 array ] , then the value of A^4 is

NDA 2017 Solution View → 89

What is the order of

NDA 2017 Solution View → 90

If A is semy square matrix of order 3 and A=5 , then what is [(2 A)^ -1 ] equal to?

NDA 2016 Solution View → 91

What is [ array lll x & y & z array ][ array lll a & h & g h & b & f g & f & c array ] equal to?

NDA 2016 Solution View → 92

If m=[ array ll 1 & 0 0 & 1 array ] and n=[ array ll 0 & 1 -1 & 0 array ] , then what is the value of the determinant of m θ-n θ ?

NDA 2016 Solution View → 93

A=[ array rr 1 & -1 2 & 3 array ] and B=[ array rr 2 & 3 -1 & -2 array ] , then which of the following is/are correct? 1. AB (A^ -1 B^ -1 ) is a unit matrix. 2. ( AB)^ -1 =A^ -1

NDA 2016 Solution View → 94

If f\ x\ =[ array ccc x & - x & 0 x & x & 0 0 & 0 & 1 array ] , then which of the following are correct? 1. f(θ) × f(φ)=f(θ+φ) 2. The value of the determinant of the matrix f(θ) ×

NDA 2016 Solution View → 95

Consider the following in respect of the matrix A=( array cc -1 & 1 1 & -1 array ) 1. A^2=-A 2. A^3=4 ~A Which of the above is/are correct?

NDA 2016 Solution View → 96

If A is a square matrix, then what is adj(A^ -1 )-(adj A)^ -1 equal to?

NDA 2016 Solution View → 97

If A=[ array ccc 1 & 1 & -1 2 & -3 & 4 3 & -2 & 3 array ] and B=[ array ccc -1 & -2 & -1 6 & 12 & 6 5 & 10 & 5 array ] then which of the following is/are correct? 1. A and B

NDA 2015 Solution View → 98

If A=[ array ccc 1 & 0 & -2 2 & -3 & 4 array ] , then the matrix X for which 2 X+3 A=0 holds true is

NDA 2015 Solution View → 99

If A is an invertible matrix of order n and k is any positive real number, then the value of [ (k A)]^ -1 A is

NDA 2015 Solution View → 100

Which one of the following matrices is an elementary matrix?

NDA 2015 Solution View → 101

The matrix [ array cc 0 & -4+i 4+i & 0 array ] is

NDA 2015 Solution View → 102

Let A= [ array cc x+y & y 2 x & x-y array ], B=[ array c 2 -1 array ] and C= [ array l 3 2 array ] If A B=C , then what is A^2 equal to?

NDA 2015 Solution View → 103

If E(θ)=[ array cc θ & θ - θ & θ array ] , then E(α) E(β) is equal to

NDA 2015 Solution View → 104

If A is an orthogonal matrix of order 3 and B=[ array ccc 1 & 2 & 3 -3 & 0 & 2 2 & 5 & 0 array ] , then which of the following is/are correct? 1. |AB|= ± 47 2. AB=BA Select the

NDA 2015 Solution View → 105

Consider the following in respect of two non-singular matrices A and B of same order: 1. (A+B)= A+ B 2. (A+B)^ -1 =A^ -1 +B^ -1 Which of the above is/are correct?

NDA 2015 Solution View → 106

If X=[ array ll 3 & -4 1 & -1 array ], B=[ array cc 5 & 2 -2 & 1 array ] and A=[ array ll p & q r & s array ] satisfy the equation A X=B , then the matrix A is equal to

NDA 2015 Solution View → 107

If A=[ array ll 2 & 7 1 & 5 array ] then that is A+3 A^ -1 equal to? where I is the identity matrix order 2.

NDA 2015 Solution View → 108

Let A and B be two matrices such that A B=A and BA=B . Which of the following statements are correct? 1. A^2=A 2. B^2=B 3. (AB)^2=AB Select the correct answer using the code given

NDA 2014 Solution View → 109

If the matrix A is such that ( array ll 1 & 3 0 & 1 array ) A=( array cc 1 & 1 0 & -1 array ) , then what is A equal to?

NDA 2014 Solution View → 110

If A is an invertible matrix, then what is (A^ -1 ) equal to?

NDA 2014 Solution View → 111

From the matrix equation AB=AC , where A, B, C are the square matrices of same order, we can conclude B=C provided

NDA 2014 Solution View → 112

If A=( array cc 4 & x+2 2 x-2 & x+1 array ) is symmetric, then what is x equal to?

NDA 2014 Solution View → 113

Consider the following statements in respect of the matrix A=[ array rrr 0 & 1 & 2 -1 & 0 & -3 -2 & 3 & 0 array ] 1. The matrix A is skew-symmetric. 2. The matrix A is symmetric.

NDA 2014 Solution View → 114

Consider two matrices A=[ array ll 1 & 2 2 & 1 1 & 1 array ] and B=[ array lll 1 & 2 & -4 2 & 1 & -4 array ] . Which one of the following is correct?

NDA 2014 Solution View → 115

If A is any matrix, then the product A A is defined only when A is a matrix of order m × n where

NDA 2014 Solution View → 116

Consider the following statements: 1. The product of two non-zero matrices can never be identity matrix. 2. The product of two non-zero matrices can never be zero matrix. Which of

NDA 2013 Solution View → 117

If A is a square matrix of order 3 with |A| ≠ 0 , then which one of the following is correct?

NDA 2013 Solution View → 118

If A=( array cc i & 0 0 & -i array ), B=( array cc 0 & -1 1 & 0 array ), C=( array cc 0 & i i & 0 array ) where i= -1 , then which one of the following is correct?

NDA 2013 Solution View → 119

If 2 A=( array ll 2 & 1 3 & 2 array ) , then what is A^ -1 equal to?

NDA 2013 Solution View → 120

If ( array ll 2 & 3 4 & 1 array ) × ( array cc 5 & -2 -3 & 1 array )= ( array cc 1 & -1 17 & λ array ) then what is λ equal to?

NDA 2013 Solution View → 121

If A and B are two non-singular square matrices such that AB=A , then which one of the following is correct

NDA 2013 Solution View → 122

The determinant of an orthogonal matrix is

NDA 2013 Solution View → 123

Consider the following statements: 1. A matrix is not a number 2. Two determinants of different orders may have the same value. Which of the above statements is/are correct?

NDA 2013 Solution View → 124

The inverse of a diagonal matrix is a :

NDA 2012 Solution View → 125

If A=[ array ll 3 & 4 5 & 6 7 & 8 array ] and B=[ array lll 3 & 5 & 7 4 & 6 & 8 array ] , then which one of the following is correct?

NDA 2012 Solution View → 126

If the sum of matrices [ array l x x y array ],[ array l y y z array ] and [ array l z 0 0 array ] is the matrix [ array c 10 5 5 array ] , then what is the value of y ?

NDA 2012 Solution View → 127

If the matrix AB is a zero matrix, then which one of the following is correct?

NDA 2012 Solution View → 128

A square matrix [a_ i j ] such that a_ i j =0 for i ≠ j and a_ i j =k where k is a constant for i=j is called :

NDA 2012 Solution View → 129

If a matrix A has inverses B and C , then which one of the following is correct?

NDA 2012 Solution View → 130

A and B are two matrices such that AB=A and BA=B then what is B^2 equal to? where I is the identity matrix

NDA 2012 Solution View → 131

Consider the following statements: 1. Every zero matrix is a square matrix. 2. A matrix has a numerical value. 3. A unit matrix is a diagonal matrix. Which of the above statements

NDA 2012 Solution View → 132

If A=[ array ll 1 & 2 1 & 1 array ] and B=[ array cc 0 & -1 1 & 2 array ] , then what is B^ -1 A^ -1 equal to?

NDA 2012 Solution View → 133

What is the order of the product [ array lll x & y & z array ][ array lll a & h & g h & b & f g & f & c array ][ array l x y z array ] ?

NDA 2012 Solution View → 134

If A is a square matrix such that A^2=1 where I is the identity matrix, then what is A^ -1 equal to?

NDA 2012 Solution View → 135

The sum and product of matrices A and B exist. Which of the following implications are necessarily true? 1. A and B are square matrices of same order. 2. A and B are non-singular

NDA 2012 Solution View → 136

If A=( array ll 1 & 2 2 & 3 array ) and B=( array ll 1 & 0 1 & 0 array ) then what is determinant of A B ?

NDA 2012 Solution View → 137

Consider the following statements in respect of the square matrices A and B of same order: 1. A and B are non-zero and A B=0 ⇒ either |A|=0 or |B|=0 2. AB=0 ⇒ A=0 or B=0 Which of

NDA 2011 Solution View → 138

For what value of x does ( array lll 1 & 3 & 2 array )( array lll 1 & 3 & 0 3 & 0 & 2 2 & 0 & 1 array )( array l 0 3 x array )=(0) hold?

NDA 2011 Solution View → 139

Consider the following statements: 1. The inverse of a square matrix, if exists, is unique. 2. If A and B are singular matrices of order n , then A B is also a singular matrix of

NDA 2011 Solution View → 140

If the matrix A=[ array ll α & β β & α array ] is such that A^2=1 , then which one of the following is correct?

NDA 2011 Solution View → 141

If A=[ array ll α & 0 1 & 1 array ] and B=[ array ll 1 & 0 2 & 1 array ] such that A^2=B , then what is the value of α ?

NDA 2011 Solution View → 142

If A=[ array ll 3 & 1 0 & 4 array ] and B=[ array ll 1 & 1 0 & 2 array ] then which of the following is/are correct? 1. A B is defined 2. B A is defined 3. A B=B A Select the

NDA 2011 Solution View → 143

If a matrix A is such that 3 A^3+2 A^2+5 A+I=0 Then what is A^ -1 equal to?

NDA 2010 Solution View → 144

Let A and B be matrices of order 3 × 3 . If A B=0 , then which of the following can be concluded?

NDA 2010 Solution View → 145

If A is a square matrix, then what is adj A^T-(adj A)^T equal to ?

NDA 2010 Solution View → 146

If [ array ccc 1 & -3 & 2 2 & -8 & 5 4 & 2 & λ array ] is not an invertible matrix, then what is the value of λ ?

NDA 2010 Solution View → 147

If A=[ array cc 0 & 1 -1 & 0 array ], B=[ array cc i & 0 0 & -i array ], C=[ array cc 0 & -i -i & 0 array ] then which one of the following is not correct?

NDA 2010 Solution View → 148

If |A|=8 , where A is a square matrix of order 3 , then what is |adj A| equal to ?

NDA 2010 Solution View → 149

Let A=[ array ll 1 & 2 3 & 4 array ]=[a_ i j ] , where i, j,=1,2 . If its inverse matrix is [b_ i j ] , what is b_ 22 ?

NDA 2010 Solution View → 150

Let A=( array ccc 5 & 6 & 1 2 & -1 & 5 array ) . Let there exist a matrix B such that AB=( array ll 35 & 49 29 & 13 array ) . What is B equal to?

NDA 2010 Solution View → 151

Consider the following statements: I. If A^ =A , then A is a singular matrix, where A^ is the transpose of A. II. If A is a square matrix such that A^3=I , then A is non-singular.

NDA 2010 Solution View → 152

If A be a real skew-symmetric matrix of order n such that A^2+I=O , I being the identity matrix of the same order as that of A , then what is the order of A ?

NDA 2010 Solution View → 153

Consider the following statements in respect of a square matrix A and its transpose A^T . 1. A+A^T is always symmetric. 2. A-A^T is always anti-symmetric. Which of the statements

NDA 2010 Solution View →
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Related NDA Mathematics chapters

Trigonometric Ratios & Identities (295)Statistics (236)Probability (201)Sequences and Series (182)Three Dimensional Geometry (176)Quadratic Equation (157)Determinants (130)Functions (129)Permutation and Combination (129)Differential Equations (127)Definite Integration (110)Differentiation (104)

Matrices in other exams

JEE Matrices (506)BITSAT Matrices (19)