Problem

1. $A = \begin{pmatrix} 3 & a \\ -2 & -2 \end{pmatrix}$

where $a$ is a non-zero constant and $a \neq 3$

(a) Determine $A^{-1}$ giving your answer in terms of $a$.

Given that $A + A^{-1} = I$ where $I$ is the $2 \times 2$ identity matrix,

(b) determine the value of $a$.