3.
$$\mathbf { A } = \left( \begin{array} { l l }
4 & - 2
a & - 3
\end{array} \right)$$
where \(a\) is a real constant and \(a \neq 6\)
- Find \(\mathbf { A } ^ { - 1 }\) in terms of \(a\).
Given that \(\mathbf { A } + 2 \mathbf { A } ^ { - 1 } = \mathbf { I }\), where \(\mathbf { I }\) is the \(2 \times 2\) identity matrix,
- find the value of \(a\).