5 Let \(k\) be a constant. The matrices \(\mathbf { A } , \mathbf { B }\) and \(\mathbf { C }\) are given by $$\mathbf { A } = \left( \begin{array} { l l l } 1 & k & 3
2 & 1 & 3
3 & 2 & 5 \end{array} \right) , \quad \mathbf { B } = \left( \begin{array} { r r } 0 & - 2
- 1 & 3
0 & 0 \end{array} \right) \quad \text { and } \quad \mathbf { C } = \left( \begin{array} { r r r } - 2 & - 1 & 1
1 & 1 & 3 \end{array} \right)$$ It is given that \(\mathbf { A }\) is singular.

1. Show that \(\mathbf { C A B } = \left( \begin{array} { r r } 3 & - 7
   - 9 & 3 \end{array} \right)\).
2. Find the equations of the invariant lines, through the origin, of the transformation in the \(x - y\) plane represented by \(\mathbf { C A B }\).
3. The matrices \(\mathbf { D } , \mathbf { E }\) and \(\mathbf { F }\) represent geometrical transformations in the \(x - y\) plane.
   • D represents an enlargement, centre the origin.
   • E represents a stretch parallel to the \(x\)-axis.
   • F represents a reflection in the line \(y = x\).
   Given that \(\mathbf { C A B } = \mathbf { D } - 9 \mathbf { E F }\), find \(\mathbf { D } , \mathbf { E }\) and \(\mathbf { F }\).