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.