Exercise:
\[\]
\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Identity Matrix?} \\
\hline
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix} & ? \\
\hline
\end{array}
\]
Solution:
\[\]
\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Identity Matrix?} \\
\hline
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & \text{No} \\
\hline
\begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & \text{No} \\
\hline
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & \text{No} \\
\hline
\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix} & \text{No} \\
\hline
\end{array}
\]