Question

Let $A$ be a $2\times 2$ matrix and $B=A+A^T$. Then show that $B$ is a symmetric matrix.

Answer 1

Given,

$A$ be a $2\times 2$ matrix and $B=A+A^T$.

Now $B^T=A^T+A=B$.

Since $B^T=B$.

This given $B$ is a symmetric matrix.