1 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are defined by
$$\mathbf { A } = \left[ \begin{array} { l l }
3 & 4
4 & 3
\end{array} \right] \quad \mathbf { B } = \left[ \begin{array} { l l }
0 & 2
2 & 0
\end{array} \right]$$
- Calculate the matrices:
- \(\mathbf { A } + \mathbf { B }\);
- \(\mathbf { A B }\).
- Show that \(\mathbf { A } + \mathbf { B } - \mathbf { A B } = k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
(2 marks)