8.
$$\mathbf { A } = \left( \begin{array} { c c }
6 & - 2
- 4 & 1
\end{array} \right)$$
and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
- Prove that
$$\mathbf { A } ^ { 2 } = 7 \mathbf { A } + 2 \mathbf { I }$$
- Hence show that
$$\mathbf { A } ^ { - 1 } = \frac { 1 } { 2 } ( \mathbf { A } - 7 \mathbf { I } )$$
The transformation represented by \(\mathbf { A }\) maps the point \(P\) onto the point \(Q\).
Given that \(Q\) has coordinates \(( 2 k + 8 , - 2 k - 5 )\), where \(k\) is a constant, - find, in terms of \(k\), the coordinates of \(P\).