2 The matrices \(\mathbf { A }\) and \(\mathbf { I }\) are given by \(\mathbf { A } = \left( \begin{array} { l l } 1 & 2
1 & 3 \end{array} \right)\) and \(\mathbf { I } = \left( \begin{array} { l l } 1 & 0
0 & 1 \end{array} \right)\) respectively.
- Find \(\mathbf { A } ^ { 2 }\) and verify that \(\mathbf { A } ^ { 2 } = 4 \mathbf { A } - \mathbf { I }\).
- Hence, or otherwise, show that \(\mathbf { A } ^ { - 1 } = 4 \mathbf { I } - \mathbf { A }\).