设 $\boldsymbol{A}, \boldsymbol{P}$ 均为 3 阶矩阵， $\boldsymbol{P}^{\mathrm{T}}$ 为 $\boldsymbol{P}$ 的转置矩阵，且 $\boldsymbol{P}^{\mathrm{T}} \boldsymbol{A} \boldsymbol{P}=\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$ ，若 $\boldsymbol{P}=\left(\boldsymbol{\alpha}_1\right.$ ， $\left.\alpha_2, \alpha_3\right), Q=\left(\alpha_1+\alpha_2, \alpha_2, \alpha_3\right)$ ，则 $Q^{\mathrm{T}} A Q$ 为
A. $\left(\begin{array}{lll}2 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$ ．
B. $\left(\begin{array}{lll}1 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2\end{array}\right)$ ．
C. $\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$ ．
D. $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right)$ ．