设矩阵 $\boldsymbol{A}=\left(\begin{array}{lll}a & b & b \\ b & a & b \\ b & b & a\end{array}\right), \boldsymbol{B}=\left(\begin{array}{lll}b & b & a \\ b & a & b \\ a & b & b\end{array}\right), \boldsymbol{C}=\left(\begin{array}{lll}b & a & b \\ a & b & b \\ b & b & a\end{array}\right), \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}$ 均可逆，则
A. $\boldsymbol{A}, \boldsymbol{B}$ 不相似但合同．
B. $\boldsymbol{B}, \boldsymbol{C}$ 既相似又合同．
C. $\boldsymbol{A}, \boldsymbol{C}$ 不相似但合同．
D. $\boldsymbol{B}, \boldsymbol{C}$ 不相似但合同．