JAMB 2010 · UTME · Q27

If $P = \begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}$ , what is $P^{-1}$ ?

Worked solution (try it first)

The determinant is $|P| = 2 \times 1 - (-3) \times 1 = 5$ .
Swap the two diagonal entries (2 and 1) and change the signs of the other two ( $-3$ becomes 3, and 1 becomes $-1$ ): $\begin{pmatrix} 1 & 3 \\ -1 & 2 \end{pmatrix}$ .
Divide every entry by 5: $P^{-1} = \begin{pmatrix} \frac15 & \frac35 \\ -\frac15 & \frac25 \end{pmatrix}$ , option B.