#### Let A and B be two symmetric matrices of order 3 .Statement -1 : and   are symmetric matrices.Statement -2 :   is symmetric matrix if matrix multiplication of A and B is commutative. Option 1) Statement-1 is true, Statement-2 is false. Option 2) Statement-1 is false, Statement-2 is true. Option 3) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 . Option 4) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

As we learnt in

Property of Transpose Conjugate -

- wherein

is the conjugate matrix of

Given that

Then

Similarly

AB is symmmetric matrix.

If AB is commulative.

Option 1)

Statement-1 is true, Statement-2 is false.

Incorrect Option

Option 2)

Statement-1 is false, Statement-2 is true.

Incorrect Option

Option 3)

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

Incorrect Option

Option 4)

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

Correct Option