9. With reference to a fixed origin \(O\) and coordinate axes \(O x\) and \(O y\), a transformation from \(\mathbb { R } ^ { 2 } \rightarrow \mathbb { R } ^ { 2 }\) is represented by the matrix \(A\) where
$$A = \left( \begin{array} { c c }
3 & 1
1 & - 2
\end{array} \right)$$
- Find \(\mathrm { A } ^ { 2 }\).
- Show that the matrix A is non-singular.
- Find \(\mathrm { A } ^ { - 1 }\).
The transformation represented by matrix A maps the point \(P\) onto the point \(Q\).
Given that \(Q\) has coordinates \(( k - 1,2 - k )\), where \(k\) is a constant, - show that \(P\) lies on the line with equation \(y = 4 x - 1\)