设 $\left(\begin{array}{lll}a & 1 & 1 \\ 1 & a & 1 \\ 1 & 1 & a\end{array}\right)\left(\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right)=\left(\begin{array}{c}1 \\ 1 \\ -2\end{array}\right)$ 有无穷多个解，则 $a=$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$