If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.
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Correct Answer: Option C
Explanation:
\(\begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix} \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\)
= \(\begin{pmatrix} 1\times 0 + 2\times 1 & 1\times 1 + 2\times3 \\ 5\times0 + 1\times1 & 5\times1 + 1\times 3 \end{pmatrix}\)
= \(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)
\(\begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix} \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\)
= \(\begin{pmatrix} 1\times 0 + 2\times 1 & 1\times 1 + 2\times3 \\ 5\times0 + 1\times1 & 5\times1 + 1\times 3 \end{pmatrix}\)
= \(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)