Square Matrix Exercise (with Solution)

Exercise

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Square Matrix?} \\
\hline
\begin{pmatrix} 2 & 4 & 6 \\ 1 & 3 & 5 \\ 7 & 8 & 9 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 3 & 1 & 4 \\ 2 & 5 & 7 \\ 8 & 9 & 6 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} x & y \\ z & w \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 5 & 6 \\ 7 & 8 \\ 9 & 10 \end{pmatrix} & ? \\
\hline
\end{array}
\]

Solution:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Square Matrix?} \\
\hline
\begin{pmatrix} 2 & 4 & 6 \\ 1 & 3 & 5 \\ 7 & 8 & 9 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} & \text{No} \\
\hline
\begin{pmatrix} 3 & 1 & 4 \\ 2 & 5 & 7 \\ 8 & 9 & 6 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} x & y \\ z & w \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 5 & 6 \\ 7 & 8 \\ 9 & 10 \end{pmatrix} & \text{No} \\
\hline
\end{array}
\]