2 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are defined by
$$\mathbf { A } = \left[ \begin{array} { c c }
p & 2
4 & p
\end{array} \right] \quad \mathbf { B } = \left[ \begin{array} { l l }
3 & 1
2 & 3
\end{array} \right]$$
- Find, in terms of \(p\), the matrices:
- \(\mathbf { A } - \mathbf { B }\);
- AB .
- Show that there is a value of \(p\) for which \(\mathbf { A } - \mathbf { B } + \mathbf { A B } = k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix, and state the corresponding value of \(k\).