3. The matrix \(\mathbf { R }\) is given by \(\mathbf { R } = \left( \begin{array} { c c } \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } }
- \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } } \end{array} \right)\)
- Find \(\mathbf { R } ^ { 2 }\).
- Describe the geometrical transformation represented by \(\mathbf { R } ^ { 2 }\).
- Describe the geometrical transformation represented by \(\mathbf { R }\).