设 $\boldsymbol{A}, \boldsymbol{B}$ 为 3 阶方阵, $\boldsymbol{A x}=0$ 有非零解, $\boldsymbol{B} \neq \boldsymbol{O}, \operatorname{tr}(\boldsymbol{A})=1$, 且 $\boldsymbol{A B}+\boldsymbol{B}=\boldsymbol{O}$, 则与 $(\boldsymbol{A}-\boldsymbol{E})^{\cdot}$ 相 似的对角矩阵为
A. $\left(\begin{array}{ccc}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 2\end{array}\right)$
B. $\left(\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 1\end{array}\right)$
C. $\left(\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 2\end{array}\right)$
D. $\left(\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right)$