10. The matrix \(\mathbf { A }\) is defined by
$$\mathbf { A } = \left( \begin{array} { r r r }
4 & 8 & 0
0 & \lambda & - 2
4 & 0 & \lambda
\end{array} \right)$$
- Show that there are two values of \(\lambda\) for which \(\mathbf { A }\) is singular.
- Given that \(\lambda = 3\),
- determine the adjugate matrix of \(\mathbf { A }\),
- determine the inverse matrix \(\mathbf { A } ^ { - 1 }\).