1 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by $$\mathbf { A } = \left[ \begin{array} { l l } 2 & 1
3 & 8 \end{array} \right] , \quad \mathbf { B } = \left[ \begin{array} { l l } 1 & 2
3 & 4 \end{array} \right]$$ The matrix \(\mathbf { M } = \mathbf { A } - 2 \mathbf { B }\).

1. Show that \(\mathbf { M } = n \left[ \begin{array} { r r } 0 & - 1
   - 1 & 0 \end{array} \right]\), where \(n\) is a positive integer.
   (2 marks)
2. The matrix \(\mathbf { M }\) represents a combination of an enlargement of scale factor \(p\) and a reflection in a line \(L\). State the value of \(p\) and write down the equation of \(L\).
3. Show that $$\mathbf { M } ^ { 2 } = q \mathbf { I }$$ where \(q\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix.