Let A and B 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 with B is commutative.

Options

A. Statement 1 is false, statement 2 is true.
B. Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1.
C. Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1.
D. Statement 1 is true, statement 2 is false.

Answer

C

Explanation

`(A(BA))^(T)=(BA)^(T) A^(T)`
`=(A^(T) B^(T)).A^(T)`
`=(AB) A`
`=A(BA)`
Similarly `((AB)A)^(T)=(AB)A`
Clearly both statements are true but statement 2 is not a correct explanation of statement 1.