Question

Let $A$ being a square matrix, then prove that $A+A^T$ is symmetric.

Answer 1

Let $B=A+A^T$.

Now,

$B^T$

$=(A+A^T{)}^T$

$=A^T+(A^T{)}^T$

$=A^T+A$ [ Since $(A^T{)}^T=A$]

$=B$.

So, $A+A^T$s a symmetric matrix.