Identity Matrix Exercise (with Solution)

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:

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

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