Determining Symmetry of Matrix F: ABA

[mvpshaq32]

Homework Statement

Let A and B be symmetric n x n matrices. Determine whether the given matrix must be symmetric or could be nonsymmetric.

F=ABA

Homework Equations

(AB)^T=B^T A^t

The Attempt at a Solution

So if it's symmetric, that means (ABA)^T=ABA. I decided to make A one term and BA another term and distributed it to be (BA)^T (A)^T=A^T B^T A^T=ABA, making it symmetric.
But I'm not sure if I can evaluate it like this.

 

[Dick]

That looks perfectly ok to me.

 

[mvpshaq32]

That looks perfectly ok to me.

Thanks very much!