Question

Assertion (A): For any symmetric matrix A, B’AB is a skew-symmetric matrix.

Reason (R): A square matrix P is skew-symmetric if P’ = – P.

(A) Both Assertion (A) and Reason (R) are true and 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 true, but Reason (R) is false.

(D) Assertion (A) is false, but Reason (R) is true.

Answer 1

Correct option is (D) Assertion (A) is false, but Reason (R) is true.

If A is symmetric matrix then A' = A  ........(1)

Now (B'AB)' = [B'(AB)]'

= (AB)'(B')'  (by using formula (AB)' = B'A') 

= B'A'B 

= B'AB    (by substituting (1)) 

Which gives B'AB is symmetric matrix. So Assertion (A) is false.

By definition a square matrix A is said to be skew-symmetric if A' = -A. So Reason (R) is true.