6 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by
$$\mathbf { A } = \left[ \begin{array} { l l }
0 & 2
2 & 0
\end{array} \right] , \quad \mathbf { B } = \left[ \begin{array} { r r }
2 & 0
0 & - 2
\end{array} \right]$$
- Calculate the matrix \(\mathbf { A B }\).
- Show that \(\mathbf { A } ^ { 2 }\) is of the form \(k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
- Show that \(( \mathbf { A B } ) ^ { 2 } \neq \mathbf { A } ^ { 2 } \mathbf { B } ^ { 2 }\).