WAEC 2023 · Paper 1 · Q21

A linear transformation on the $oxy$ plane is defined by $P: (x, y) \rightarrow (2x + y, -2y)$ . Find $P^2$ .

Worked solution (try it first)

Read the matrix from the images: $x$ goes to $2x + y$ and $y$ goes to $-2y$ , so $P = \begin{pmatrix} 2 & 1 \\ 0 & -2 \end{pmatrix}$ .
Multiply $P$ by itself.
Top row: $(2)(2) + (1)(0) = 4$ and $(2)(1) + (1)(-2) = 0$ .
Bottom row: $(0)(2) + (-2)(0) = 0$ and $(0)(1) + (-2)(-2) = 4$ .
So $P^2 = \begin{pmatrix} 4 & 0 \\ 0 & 4 \end{pmatrix}$ , option C.