4 The group \(G\) consists of a set of six matrices under matrix multiplication. Two of the elements of \(G\) are \(\mathbf { A } = \left( \begin{array} { l l } 0 & 1
1 & 0 \end{array} \right)\) and \(\mathbf { B } = \left( \begin{array} { l l } 1 & - 1
0 & - 1 \end{array} \right)\).
- Determine each of the following:
- \(\mathbf { A } ^ { 2 }\)
- \(\mathbf { B } ^ { 2 }\)
- Determine all the elements of \(G\).
- State the order of each non-identity element of \(G\).
- State, with justification, whether \(G\) is
- abelian
- cyclic.