If \(P = \begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\), find PQ.
A. \(\begin{pmatrix} 4 & 1 \\ -2 & 9 \end{pmatrix}\)
B. \(\begin{pmatrix} -4 & 1 \\ 2 & 9 \end{pmatrix}\)
C. \(\begin{pmatrix} -4 & 3 \\ -2 & 13 \end{pmatrix}\)
D. \(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)
Correct Answer: D
Explanation
\(\begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix} \(\begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\)
= \(\begin{pmatrix} (1 \times -2) + (-2 \times 1) & (1 \times 3) + (-2 \times 0) \\ (3 \times -2) + (4 \times 1) & (3 \times 3) + (4 \times 0) \end{pmatrix}\)
= \(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)
