Matrix Equality Exercise (with Solution)

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix Equality Question} & \textbf{Equality (Yes/No)} \\
\hline
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\
\hline
C = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix}, D = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix} & ? \\
\hline
E = \begin{pmatrix} 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix}, F = \begin{pmatrix} 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix} & ? \\
\hline
G = \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}, H = \begin{pmatrix} 6 & 7 \\ 8 & 9 \end{pmatrix} & ? \\
\hline
I = \begin{pmatrix} 1 & 4 \\ 5 & 8 \end{pmatrix}, J = \begin{pmatrix} 1 & 4 \\ 6 & 8 \end{pmatrix} & ? \\
\hline
K = \begin{pmatrix} 3 & 2 \\ 7 & 6 \end{pmatrix}, L = \begin{pmatrix} 3 & 2 \\ 7 & 6 \end{pmatrix} & ? \\
\hline
\end{array}
\]

Solution:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix Equality Question} & \textbf{Equality (Yes/No)} \\
\hline
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & \text{Yes} \\
\hline
C = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix}, D = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix} & \text{Yes} \\
\hline
E = \begin{pmatrix} 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix}, F = \begin{pmatrix} 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix} & \text{Yes} \\
\hline
G = \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}, H = \begin{pmatrix} 6 & 7 \\ 8 & 9 \end{pmatrix} & \text{No} \\
\hline
I = \begin{pmatrix} 1 & 4 \\ 5 & 8 \end{pmatrix}, J = \begin{pmatrix} 1 & 4 \\ 6 & 8 \end{pmatrix} & \text{No} \\
\hline
K = \begin{pmatrix} 3 & 2 \\ 7 & 6 \end{pmatrix}, L = \begin{pmatrix} 3 & 2 \\ 7 & 6 \end{pmatrix} & \text{Yes} \\
\hline
\end{array}
\]