设向量 $\alpha_1=\left(\begin{array}{c}a \\ 1 \\ -1 \\ 1\end{array}\right), \alpha_2=\left(\begin{array}{l}1 \\ 1 \\ b \\ a\end{array}\right), \alpha_3=\left(\begin{array}{c}1 \\ a \\ -1 \\ 1\end{array}\right)$, 若 $\alpha_1, \alpha_2, \alpha_3$ 线性相关，且其中任意两个向量均线性无关，则（）
$\text{A.}$ $a=1, b \neq-1$
$\text{B.}$ $a=1, b=-1$
$\text{C.}$ $a \neq-2, b=2$
$\text{D.}$ $a=-2, b=2$