9 The matrix \(\mathbf { R }\) is \(\left( \begin{array} { r r } 0 & - 1
1 & 0 \end{array} \right)\).
- Explain in terms of transformations why \(\mathbf { R } ^ { 4 } = \mathbf { I }\).
- Describe the transformation represented by \(\mathbf { R } ^ { - 1 }\) and write down the matrix \(\mathbf { R } ^ { - 1 }\).
- \(\mathbf { S }\) is the matrix representing rotation through \(60 ^ { \circ }\) anticlockwise about the origin. Find \(\mathbf { S }\).
- Write down the smallest positive integers \(m\) and \(n\) such that \(\mathbf { S } ^ { m } = \mathbf { R } ^ { n }\), explaining your answer in terms of transformations.
- Find \(\mathbf { R S }\) and explain in terms of transformations why \(\mathbf { R S } = \mathbf { S R }\).
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