Matrices
(2025)
Q.1 If A and B are square matrices of same order such that AB = A and BA = B,
then A2 + B2 is equal to :
(1 Mark) (CBSE 2025 - 65/4/1)
A. A + B
B. 2 BA
C. BA
D. 2(A + B)
Q.2
(1 Mark) (CBSE 2025 - 65/4/1)
A. diagonal matrix
B. skew symmetric matrix
C. symmetric matrix
D. scalar matrix
Q.3 Let both AB′ and B′A be defined for matrices A and B. If order of A is n × m,
then the order of B is :
(1 Mark) (CBSE 2025 - 65/6/1)
A. m × n
B. n × m
,C. n × n
D. m × m
Q.4
(1 Mark) (CBSE 2025 - 65/6/1)
A. identity matrix
B. scalar matrix
C. skew-symmetric matrix
D. symmetric matrix
Q.5 Sum of two skew-symmetric matrices of same order is always a/an :
(1 Mark) (CBSE 2025 - 65/6/1)
A. identity matrix
B. symmetric matrix
C. null matrix
D. skew-symmetric matrix
Q.6
, (1 Mark) (CBSE 2025 - 65/2/1)
A. 6
B. 8
C. -8
D. 0
Q.7 Which of the following can be both a symmetric and skew-symmetric
matrix?
(1 Mark) (CBSE 2025 - 65/2/1)
A. Diagonal Matrix
B. Unit Matrix
C. Row Matrix
D. Null Matrix
Q.8 Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4AB +
3(AB + BA)−4BA, where A and B are both matrices of order 2 × 2. It is known
that Aeq BeqI and A−1eqB.
(1 Mark) (CBSE 2025 - 65/2/1)
, Q.9 If A and B are square matrices of order mm such that A2 − B2 = (A − B) (A
+ B), then which of the following is always correct?
(1 Mark) (CBSE 2025 - 65/2/1)
A. A = B
B. A = I or B = I
C. A = 0 or B=0
D. AB = BA
Q.10
Reason ® : If a diagonal matrix has all non-zero elements equal, it is known as a
scalar matrix.
(1 Mark) (CBSE 2025 - 65/2/1)
A. Both Assertion (A) and Reason (R) are true and the Reason (R) is the
correct explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
C. Assertion (A) is false but Reason (R) is true.
D. Assertion (A) is true but Reason (R) is false.
Q.11 What is the total number of possible matrices of order 3 × 3 with each
entry as √2 or √3 ?
(1 Mark) (CBSE 2025 - 65/7/1)
A. 9
B. 615
(2025)
Q.1 If A and B are square matrices of same order such that AB = A and BA = B,
then A2 + B2 is equal to :
(1 Mark) (CBSE 2025 - 65/4/1)
A. A + B
B. 2 BA
C. BA
D. 2(A + B)
Q.2
(1 Mark) (CBSE 2025 - 65/4/1)
A. diagonal matrix
B. skew symmetric matrix
C. symmetric matrix
D. scalar matrix
Q.3 Let both AB′ and B′A be defined for matrices A and B. If order of A is n × m,
then the order of B is :
(1 Mark) (CBSE 2025 - 65/6/1)
A. m × n
B. n × m
,C. n × n
D. m × m
Q.4
(1 Mark) (CBSE 2025 - 65/6/1)
A. identity matrix
B. scalar matrix
C. skew-symmetric matrix
D. symmetric matrix
Q.5 Sum of two skew-symmetric matrices of same order is always a/an :
(1 Mark) (CBSE 2025 - 65/6/1)
A. identity matrix
B. symmetric matrix
C. null matrix
D. skew-symmetric matrix
Q.6
, (1 Mark) (CBSE 2025 - 65/2/1)
A. 6
B. 8
C. -8
D. 0
Q.7 Which of the following can be both a symmetric and skew-symmetric
matrix?
(1 Mark) (CBSE 2025 - 65/2/1)
A. Diagonal Matrix
B. Unit Matrix
C. Row Matrix
D. Null Matrix
Q.8 Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4AB +
3(AB + BA)−4BA, where A and B are both matrices of order 2 × 2. It is known
that Aeq BeqI and A−1eqB.
(1 Mark) (CBSE 2025 - 65/2/1)
, Q.9 If A and B are square matrices of order mm such that A2 − B2 = (A − B) (A
+ B), then which of the following is always correct?
(1 Mark) (CBSE 2025 - 65/2/1)
A. A = B
B. A = I or B = I
C. A = 0 or B=0
D. AB = BA
Q.10
Reason ® : If a diagonal matrix has all non-zero elements equal, it is known as a
scalar matrix.
(1 Mark) (CBSE 2025 - 65/2/1)
A. Both Assertion (A) and Reason (R) are true and the Reason (R) is the
correct explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
C. Assertion (A) is false but Reason (R) is true.
D. Assertion (A) is true but Reason (R) is false.
Q.11 What is the total number of possible matrices of order 3 × 3 with each
entry as √2 or √3 ?
(1 Mark) (CBSE 2025 - 65/7/1)
A. 9
B. 615
