1 In this question you must show detailed reasoning.
S is the 2-D transformation which is a stretch of scale factor 3 parallel to the \(x\)-axis. A is the matrix which represents S .

1. Write down \(\mathbf { A }\).
2. By considering the transformation represented by \(\mathbf { A } ^ { - 1 }\), determine the matrix \(\mathbf { A } ^ { - 1 }\). Matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \left( \begin{array} { c c } 0 & - 1
   - 1 & 0 \end{array} \right)\). T is the transformation represented by \(\mathbf { B }\).
3. Describe T.
4. Determine the matrix which represents the transformation S followed by T .
5. Demonstrate, by direct calculation, that \(( \mathbf { B A } ) ^ { - 1 } = \mathbf { A } ^ { - 1 } \mathbf { B } ^ { - 1 }\).