, By O.P. GUPTA
Indira Award Winner
M.+919650350480
Chapter 01 - Matrices & Determinants
Select the correct option (s) in the followings.
Q01. If A and B are two matrices such that A B and AB are both defined then
(a) A and B can be any matrices
(b) A and B are square matrices not necessarily of same order
(c) Number of columns in A Number of rows in B
(d) A and B are square matrices of same order.
2 1
Q02. If A then, AA T is equal to
3 1
5 5 1 1 1 1
(a) (b) 5 (c) 5 I 2 (d)
10 5 1 2 1 2
a b c
Q03. Let A d e f 4 . Then adj.A
g h i
(a) 16 (b) 2 only (c) –2 only (d) –16
x 2
Q105. If is a singular matrix, then the product of all possible values of x is
3 x 1
(a) 6 (b) 6 (c) 0 (d) 7
1
A 1
Q106. If , where A is a 3 3 matrix, then the value of k is
2 kA
1 1
(a) (b) 8 (c) 2 (d)
8 2
0 1
Q107. If A , then A 2023 is equal to
0 0
0 1 0 2023 0 0 2023 0
(a) (b) 0 (c) (d)
0 0 0 0 0
0
2023
2 0
Q108. If
5 4 P Q, where P is a symmetric and Q is a skew symmetric matrix, then Q
2 5/2 0 5/2 0 5/2 2 5/2
(a) (b) (c) (d)
5/2 4 5/2 0 5/2 0 5/2 4
Q110. If A kA , where A is a square matrix of order 2, then sum of all possible value of k is
(a) 1 (b) 1 (c) 2 (d) 0
Q111. Number of symmetric matrices of order 3 3 with each entry 1 or –1 is
(a) 512 (b) 64 (c) 8 (d) 4
436 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics
Indira Award Winner
M.+919650350480
Chapter 01 - Matrices & Determinants
Select the correct option (s) in the followings.
Q01. If A and B are two matrices such that A B and AB are both defined then
(a) A and B can be any matrices
(b) A and B are square matrices not necessarily of same order
(c) Number of columns in A Number of rows in B
(d) A and B are square matrices of same order.
2 1
Q02. If A then, AA T is equal to
3 1
5 5 1 1 1 1
(a) (b) 5 (c) 5 I 2 (d)
10 5 1 2 1 2
a b c
Q03. Let A d e f 4 . Then adj.A
g h i
(a) 16 (b) 2 only (c) –2 only (d) –16
x 2
Q105. If is a singular matrix, then the product of all possible values of x is
3 x 1
(a) 6 (b) 6 (c) 0 (d) 7
1
A 1
Q106. If , where A is a 3 3 matrix, then the value of k is
2 kA
1 1
(a) (b) 8 (c) 2 (d)
8 2
0 1
Q107. If A , then A 2023 is equal to
0 0
0 1 0 2023 0 0 2023 0
(a) (b) 0 (c) (d)
0 0 0 0 0
0
2023
2 0
Q108. If
5 4 P Q, where P is a symmetric and Q is a skew symmetric matrix, then Q
2 5/2 0 5/2 0 5/2 2 5/2
(a) (b) (c) (d)
5/2 4 5/2 0 5/2 0 5/2 4
Q110. If A kA , where A is a square matrix of order 2, then sum of all possible value of k is
(a) 1 (b) 1 (c) 2 (d) 0
Q111. Number of symmetric matrices of order 3 3 with each entry 1 or –1 is
(a) 512 (b) 64 (c) 8 (d) 4
436 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics
