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.\\
(i) Find $\mathbf { A } ^ { 2 }$ and verify that $\mathbf { A } ^ { 2 } = 4 \mathbf { A } - \mathbf { I }$.\\
(ii) Hence, or otherwise, show that $\mathbf { A } ^ { - 1 } = 4 \mathbf { I } - \mathbf { A }$.

\hfill \mbox{\textit{OCR FP1  Q2}}