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Matrices — NDA Mathematics PYQs

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

153 questionsMathematicsSolutions on every page
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 also a

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 |M₁|+|M₂|+|M₃|+ +|M₅₀| 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. Select

NDA 2026 Solution View → 5

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

NDA 2025 Solution View → 6

For the following two (02) items: Let A = pmatrix & - & 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 non

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 & - & 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( ) = pmatrix & - & pmatrix , then what is f( ) ^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 square ma

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 det ( 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

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

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 ze

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 & 2 ^2 -1 & 0 2 & 2 & 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 ⁻¹= A ^ T S

NDA 2024 Solution View → 27

If A, B and C are square matrices of order 3 and det ( BC )=2 det ( ~A ) , then what is the value of det (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 ( + ) ?

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 n

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 n

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 det (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 w

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 det [ adj ( adj A)] ?

NDA 2023 Solution View → 36

If A= ( array ccc 1 & 0 & 0 0 & & 0 & & - 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 null matrix S

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 entries.

NDA 2022 Solution View → 38

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

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 & & 0 -2 & & 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 ide

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 answ

NDA 2022 Solution View → 45

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

NDA 2022 Solution View → 46

If A= [ array ll 1 & a 0 & 1 array ] where a N , then what is A¹⁰⁰-A⁵⁰-2 A²⁵ 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 corre

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 det (A B)= det (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 det A=4 and det B=3 . Question: What is det (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 (- )- (- ) - (- ) (- ) ?

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 transpo

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.

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 & & 0 - & & 0 0 & 0 & 1 array )

NDA 2018 Solution View → 74

If A= [ array ll 1 & 2 2 & 3 array ] and A^2-k A-I₂=O , where I₂ 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. ( A )⁻¹ ~A ⁻¹ where is a scalar Select the correct answer using the co

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 & 2 2 & array ] and det (A^3 )=125 , then 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 det (B⁻¹ A B ) is equal to

NDA 2017 Solution View → 84

If A= [ array cc & - & 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 & - & 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 cons

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 det A=5 , then what is det [(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 - n ?

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 ~B

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 ( ) f ( )= f ( + ) 2. The value of the determinant of the matrix f( ) f

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 comm

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 [ det (k A)]⁻¹ det 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( )= [ array cc & - & array ] , then E( ) E( ) 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. det (A+B)= det A+ det 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 co

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 det ( 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 & array ) then what is equal to?

NDA 2013 Solution View →
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