Proving Symmetry of A + A(Transpose) for Any Square Matrix A

[HKP]

Homework Statement

Show that A + A(transpose) is symmetric for any square matrix A.

Homework Equations

A symmetric matrice is equal to A=A(transpose)

The Attempt at a Solution

I said A + A(transpose)
= A(transpose) + A(transpose)
= (A + A) (transpose)
= A + A

I don't know what else to do

 

[Mark44]

It looks like you're assuming that A is symmetric right at the start, which isn't information that you're given.

Start with the definitions of A^T and symmetric matrix.

The definition you show for a symmetric matrix isn't right - I think you want this:
A symmetric matrix A is such that A = A^T. (A matrix can't be "equal" to an equation.)