JAMB 1995 · UME · Q25

If $X = \begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}$ and $Y = \begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}$ , find $XY$ .

Worked solution (try it first)

For $XY$ , multiply each row of $X$ by each column of $Y$ .
Row 1 of $X$ is $(1, 2)$ : with column 1 it gives $2 + 8 = 10$ , and with column 2, $1 + 6 = 7$ .
Row 2 of $X$ is $(0, 3)$ : with column 1 it gives $0 + 12 = 12$ , and with column 2, $0 + 9 = 9$ .
So $XY = \begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}$ , option A.