JAMB 1999 · UME · Q15

Find the matrix $T$ if $ST = I$ , where $S = \begin{pmatrix} -1 & 1 \\ 1 & -2 \end{pmatrix}$ and $I$ is the identity matrix.

Worked solution (try it first)

$ST = I$ means $T$ is the inverse of $S$ .
The determinant is $|S| = (-1)(-2) - (1)(1) = 1$ .
For a $2 \times 2$ inverse, swap the two diagonal entries and change the signs of the other two: $\begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}$ .
Divide by the determinant, 1, which changes nothing.
So $T = \begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}$ , option B.