JAMB 2001 · UME · Q18

Given the matrix $K = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ , the matrix $K^2 + K + I$ , where $I$ is the $2 \times 2$ identity matrix, is

Worked solution (try it first)

$K^2$ means $K \times K$ , row by column: $K^2 = \begin{pmatrix} 4 + 3 & 2 + 4 \\ 6 + 12 & 3 + 16 \end{pmatrix}$
$= \begin{pmatrix} 7 & 6 \\ 18 & 19 \end{pmatrix}$ .
Add $K$ entry by entry: $\begin{pmatrix} 9 & 7 \\ 21 & 23 \end{pmatrix}$ .
$I$ adds 1 to each diagonal entry only: $\begin{pmatrix} 10 & 7 \\ 21 & 24 \end{pmatrix}$ , option B.