JAMB 2003 · UME · Q15

A matrix $P$ has inverse $P^{-1} = \begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix}$ . Find $P$ .

Worked solution (try it first)

$P$ is the inverse of $P^{-1}$ .
The determinant of $P^{-1}$ is $1 \times 1 - (-3) \times 0 = 1$ .
Swap the two diagonal entries (both 1, so no change) and change the signs of the other two: $-3$ becomes 3, and 0 stays 0.
Divide by the determinant, 1: $P = \begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix}$ , option A.