NECO 2024 · Paper 1 · Q17

If $P = \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix}$ and $Q = \begin{pmatrix} 2 & 3 \\ 2 & 1 \end{pmatrix}$ , find $PQ$ .

Worked solution (try it first)

Multiply each row of $P$ by each column of $Q$ .
Row 1 of $P$ is $(-1, 2)$ : with column 1 it gives $-2 + 4 = 2$ , and with column 2, $-3 + 2 = -1$ .
Row 2 of $P$ is $(3, 1)$ : with column 1 it gives $6 + 2 = 8$ , and with column 2, $9 + 1 = 10$ .
So $PQ = \begin{pmatrix} 2 & -1 \\ 8 & 10 \end{pmatrix}$ , option E.