7 The matrix \(\mathbf { A }\) is defined by
$$\mathbf { A } = \left[ \begin{array} { c c }
- 1 & - \sqrt { 3 }
\sqrt { 3 } & - 1
\end{array} \right]$$
- Calculate the matrix \(\mathbf { A } ^ { 2 }\).
- Show that \(\mathbf { A } ^ { 3 } = k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.
- Describe the single geometrical transformation, or combination of two geometrical transformations, corresponding to each of the matrices:
- \(\mathrm { A } ^ { 3 }\);
- A.