Given A = \(
\begin{bmatrix}
4 &1 \\[0.3em]
5 & 8 \\[0.3em]
\end{bmatrix}\).

**To Prove:** A + A’ is symmetric.(Note:A matrix P is symmetric if P’ = P)

**Proof: **We will find A’,

A' = \(
\begin{bmatrix}
4 &1 \\[0.3em]
5 & 8 \\[0.3em]
\end{bmatrix}\)

Now let us take P = A + A’

\(\Rightarrow P'=P\)

Hence A + A’ is a symmetric matrix.