Question

consider the following statements in respect of symmetric matrices A and B

Which statement is correct

. 1) AB is symmetric

2)$A^2$+ [tex]B^2 [tex]is Symmmetric

solve it by the taking

A=B=| 1 2 |
|2 4 |​

Answer 1

Answer:

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

Given, A=A

B=B

Now (A(BA))=(BA)A=(AB)A=(AB)A

=A(BA)

Similarly ((AB)A)=(AB)A

So, A(BA) and (AB)A are symmetric matrices.

Again (AB)=BA

Now if BA=AB, then AB is symmetric matrix.

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

Hence, option 'B' is correct.