设向量\(\alpha_{1}=\begin{pmatrix}a\\1\\ -1\\1\end{pmatrix}\)，\(\alpha_{2}=\begin{pmatrix}1\\1\\b\\a\end{pmatrix}\)，\(\alpha_{3}=\begin{pmatrix}1\\a\\ -1\\1\end{pmatrix}\)，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( )
A. \(a = 1,b\neq - 1\)
B. \(a = 1,b = - 1\)
C. \(a\neq - 2,b = 2\)
D. \(a = - 2,b = 2\)