设 $\boldsymbol{A}, \boldsymbol{B}$ 为 $n$ 阶矩阵,则下列结论错误的是
$\text{A.}$ 若 $\boldsymbol{A} \sim \boldsymbol{B}$, 则 $\boldsymbol{A}^m \sim \boldsymbol{B}^m$
$\text{B.}$ 若 $\boldsymbol{A} \sim \boldsymbol{B}$, 则 $\lambda \boldsymbol{E}-\boldsymbol{A} \sim \lambda \boldsymbol{E}-\boldsymbol{B}$
$\text{C.}$ 若 $\boldsymbol{A} \sim \boldsymbol{B}$ 且 $\boldsymbol{A}, \boldsymbol{B}$ 可逆, 则 $\boldsymbol{A}^{-1}+\boldsymbol{A}^* \sim \boldsymbol{B}^{-1}+\boldsymbol{B}^*$
$\text{D.}$ 若 $\boldsymbol{A} \sim \boldsymbol{B}$, 则 $\boldsymbol{A}+\boldsymbol{A}^{\mathrm{T}} \sim \boldsymbol{B}+\boldsymbol{B}^{\mathrm{T}}$