9 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l } 2 & 3
0 & 2 \end{array} \right)\).
- By considering \(\mathbf { A } , \mathbf { A } ^ { 2 } , \mathbf { A } ^ { 3 }\) and \(\mathbf { A } ^ { 4 }\) make a conjecture about the form of the matrix \(\mathbf { A } ^ { n }\) in terms of \(n\) for \(n \geqslant 1\).
- Use induction to prove the conjecture made in part (a).