5 The matrix \(\mathbf { M }\) is defined by
$$\mathbf { M } = \left[ \begin{array} { c c }
\frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } }
- \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } }
\end{array} \right]$$
- Find the matrix:
- \(\mathbf { M } ^ { 2 }\);
- \(\mathbf { M } ^ { 4 }\).
- Describe fully the geometrical transformation represented by \(\mathbf { M }\).
- Find the matrix \(\mathbf { M } ^ { 2006 }\).