The matrix \(\mathbf { X }\) is given by \(\mathbf { X } = \left( \begin{array} { l l } 1 & 2 0 & 1 \end{array} \right)\). Describe fully the geometrical transformation represented by \(\mathbf { X }\).
The matrix \(\mathbf { Z }\) is given by \(\mathbf { Z } = \left( \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 2 } ( 2 + \sqrt { 3 } ) - \frac { 1 } { 2 } \sqrt { 3 } & \frac { 1 } { 2 } ( 1 - 2 \sqrt { 3 } ) \end{array} \right)\). The transformation represented by \(\mathbf { Z }\) is equivalent to the transformation represented by \(\mathbf { X }\), followed by another transformation represented by the matrix \(\mathbf { Y }\). Find \(\mathbf { Y }\).
Describe fully the geometrical transformation represented by \(\mathbf { Y }\).