The matrices A, B and C are given by

\(A = \begin{pmatrix} 2 & k & k \\ 5 & -1 & 3 \\ 1 & 0 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 0 & 1 & 1 \\ -1 & 2 & 0 \end{pmatrix},\)

where \(k\) is a real constant.

1. Find \(CAB\).
2. Given that \(A\) is singular, find the value of \(k\).
3. Using the value of \(k\) from part (b), find the equations of the invariant lines, through the origin, of the transformation in the \(x-y\) plane represented by \(CAB\).