4 It is given that
$$\mathbf { A } = \left[ \begin{array} { l l }
1 & 4
3 & 1
\end{array} \right]$$
and that \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
- Show that \(( \mathbf { A } - \mathbf { I } ) ^ { 2 } = k \mathbf { I }\) for some integer \(k\).
- Given further that
$$\mathbf { B } = \left[ \begin{array} { l l }
1 & 3
p & 1
\end{array} \right]$$
find the integer \(p\) such that
$$( \mathbf { A } - \mathbf { B } ) ^ { 2 } = ( \mathbf { A } - \mathbf { I } ) ^ { 2 }$$