JAMB 2015 · UTME · Q37

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 $|S| = (-1)(-2) - (1)(1) = 1$ .
Swap the two diagonal entries and change the signs of the other two: $T = \begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}$ .
Check: $ST = \begin{pmatrix} 2 - 1 & 1 - 1 \\ -2 + 2 & -1 + 2 \end{pmatrix}$ , which is $I$ .
So the answer is option B.