JAMB 2004 · UME · Q22

The inverse of the matrix $\begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}$ is

Worked solution (try it first)

The determinant is $2 \times 1 - 1 \times 1 = 1$ .
Swap the two diagonal entries (2 and 1) and change the signs of the other two: $\begin{pmatrix} 1 & -1 \\ -1 & 2 \end{pmatrix}$ .
Divide by the determinant, 1, which changes nothing.
The inverse is option D.