7 Three non-singular square matrices, A, B and \(\mathbf { R }\) are such that
$$A R = B$$
The matrix \(\mathbf { R }\) represents a rotation about the \(z\)-axis through an angle \(\theta\) and
$$\mathbf { B } = \left[ \begin{array} { c c c }
- \cos \theta & \sin \theta & 0
\sin \theta & \cos \theta & 0
0 & 0 & 1
\end{array} \right]$$
7
- Show that \(\mathbf { A }\) is independent of the value of \(\theta\).
7 - Give a full description of the single transformation represented by the matrix \(\mathbf { A }\).