10 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { l l } 1 & 2
0 & 1 \end{array} \right)\).
- Find \(\mathbf { M } ^ { 2 }\) and \(\mathbf { M } ^ { 3 }\).
- Hence suggest a suitable form for the matrix \(\mathbf { M } ^ { n }\).
- Use induction to prove that your answer to part (ii) is correct.
- Describe fully the single geometrical transformation represented by \(\mathbf { M } ^ { 10 }\).