4. (i) Given that
$$\mathbf { A } = \left( \begin{array} { r r }
1 & 2
3 & - 1
4 & 5
\end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r r }
2 & - 1 & 4
1 & 3 & 1
\end{array} \right)$$
- find \(\mathbf { A B }\).
- Explain why \(\mathbf { A B } \neq \mathbf { B A }\).
(ii) Given that
$$\mathbf { C } = \left( \begin{array} { c r }
2 k & - 2
3 & k
\end{array} \right) \text {, where } k \text { is a real number }$$
find \(\mathbf { C } ^ { - 1 }\), giving your answer in terms of \(k\).