9 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l l } a & 1 & 1
1 & a & 1
1 & 1 & 2 \end{array} \right)\).
- Find, in terms of \(a\), the determinant of \(\mathbf { A }\).
- Hence find the values of \(a\) for which \(\mathbf { A }\) is singular.
- State, giving a brief reason in each case, whether the simultaneous equations
$$\begin{aligned}
a x + y + z & = 2 a
x + a y + z & = - 1
x + y + 2 z & = - 1
\end{aligned}$$
have any solutions when
(a) \(a = 0\),
(b) \(a = 1\).