JAMB 2017 · UTME · Q2

If $P = \begin{pmatrix} 2 & 1 \\ -3 & 0 \end{pmatrix}$ and $I$ is the $2 \times 2$ unit matrix, evaluate $P^2 - 2P + 4I$ .

Worked solution (try it first)

Square $P$ row by column: $P^2 = \begin{pmatrix} 4 - 3 & 2 + 0 \\ -6 + 0 & -3 + 0 \end{pmatrix}$
$= \begin{pmatrix} 1 & 2 \\ -6 & -3 \end{pmatrix}$ .
Subtract $2P = \begin{pmatrix} 4 & 2 \\ -6 & 0 \end{pmatrix}$ : $P^2 - 2P = \begin{pmatrix} -3 & 0 \\ 0 & -3 \end{pmatrix}$ .
Add $4I$ , which adds 4 to each diagonal entry: $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ , option C.