Question

Let A and B be two symmetric matrices of order 3.

Statement-1: A(BA) and (AB)A are symmetric matrices.

Statement-2: AB is symmetric matrix if matrix multiplication of A and B is commutative.

(A) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(B) Statement-1 is true, Statement-2 is false.

(C) Statement-1 is false, Statement-2 is true.

(D) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Answer 1

Answer is (A) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

 We have,

Therefore, Statement-1 is correct.

Also (AB)^T =  B^T A^T = BA = AB(since AB is commutative)

Therefore, Statement-2 is also correct, but it is not a correct explanation of Statement-1.