3. (i) Given that
$$\mathbf { A } = \left( \begin{array} { r r }
- 2 & 3
1 & 1
\end{array} \right) , \quad \mathbf { A } \mathbf { B } = \left( \begin{array} { r r r }
- 1 & 5 & 12
3 & - 5 & - 1
\end{array} \right)$$
- find \(\mathbf { A } ^ { - 1 }\)
- Hence, or otherwise, find the matrix \(\mathbf { B }\), giving your answer in its simplest form.
(ii) Given that
$$\mathbf { C } = \left( \begin{array} { r r }
0 & 1
- 1 & 0
\end{array} \right)$$ - describe fully the single geometrical transformation represented by the matrix \(\mathbf { C }\).
- Hence find the matrix \(\mathbf { C } ^ { 39 }\)