4. The transformation \(U\), represented by the \(2 \times 2\) matrix \(\mathbf { P }\), is a rotation through \(90 ^ { \circ }\) anticlockwise about the origin.
- Write down the matrix \(\mathbf { P }\).
The transformation \(V\), represented by the \(2 \times 2\) matrix \(\mathbf { Q }\), is a reflection in the line \(y = - x\).
- Write down the matrix \(\mathbf { Q }\).
Given that \(U\) followed by \(V\) is transformation \(T\), which is represented by the matrix \(\mathbf { R }\), (c) express \(\mathbf { R }\) in terms of \(\mathbf { P }\) and \(\mathbf { Q }\),
- find the matrix \(\mathbf { R }\),
- give a full geometrical description of \(T\) as a single transformation.