If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.
A. \(\begin{pmatrix} 5 & 1 \\ 16 & 5 \end{pmatrix}\)
B. \(\begin{pmatrix} 2 & 16 \\ 1 & 10 \end{pmatrix}\)
C. \(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)
D. \(\begin{pmatrix} 2 & 5 \\ -1 & -8 \end{pmatrix}\)
Correct Answer: C
Explanation
\(\begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix} \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\)
= \(\begin{pmatrix} 1\times 0 + 2\times 1 & 1\times 1 + 2\times3 \\ 5\times0 + 1\times1 & 5\times1 + 1\times 3 \end{pmatrix}\)
= \(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)
