设 $\alpha$ 为三维列向量，若 $\boldsymbol{\alpha} \boldsymbol{\alpha}^{\mathrm{T}}=\left[\begin{array}{ccc}1 & -1 & 1 \\ -1 & 1 & -1 \\ 1 & -1 & 1\end{array}\right]$ ，则 $\boldsymbol{\alpha}^{\mathrm{T}} \boldsymbol{\alpha}=$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$