Exercise
\[\]
\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Symmetric or Skew-Symmetric?} \\
\hline
\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 3 & 4 & 5 \\ 4 & 6 & 7 \\ 5 & 7 & 8 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ -2 & 4 & 5 \\ -3 & -5 & 6 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 2 & 1 \\ -1 & -2 \end{pmatrix} & ? \\
\hline
\end{array}
\]
Solution:
\[\]
\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Symmetric or Skew-Symmetric?} \\
\hline
\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & \text{Symmetric} \\
\hline
\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} & \text{Skew-Symmetric} \\
\hline
\begin{pmatrix} 3 & 4 & 5 \\ 4 & 6 & 7 \\ 5 & 7 & 8 \end{pmatrix} & \text{Symmetric} \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ -2 & 4 & 5 \\ -3 & -5 & 6 \end{pmatrix} & \text{Skew-Symmetric} \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & \text{Symmetric} \\
\hline
\begin{pmatrix} 2 & 1 \\ -1 & -2 \end{pmatrix} & \text{Skew-Symmetric} \\
\hline
\end{array}
\]
