1.
$$\mathbf { A } = \left( \begin{array} { r r }
3 & a
- 2 & - 2
\end{array} \right)$$
where \(a\) is a non-zero constant and \(a \neq 3\)
- Determine \(\mathbf { A } ^ { - 1 }\) giving your answer in terms of \(a\).
Given that \(\mathbf { A } + \mathbf { A } ^ { - 1 } = \mathbf { I }\) where \(\mathbf { I }\) is the \(2 \times 2\) identity matrix,
- determine the value of \(a\).