设 $\boldsymbol{A}, \boldsymbol{B}$ 为 $n$ 阶矩阵，记 $r(\boldsymbol{X})$ 为矩阵 $\boldsymbol{X}$ 的秩，$(\boldsymbol{X} \quad \boldsymbol{Y})$ 表示分块矩阵，则
A
$r(\boldsymbol{A} \quad \boldsymbol{A B})=r(\boldsymbol{A})$ ．
B
$r(\boldsymbol{A} \quad \boldsymbol{B A})=r(\boldsymbol{A})$ ．
C
$\mathrm{r}(\boldsymbol{A} \quad \boldsymbol{B})=\max \{\mathrm{r}(\boldsymbol{A}), \mathrm{r}(\boldsymbol{B})\}$ ．
D
$\operatorname{r}\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{B}\end{array}\right)=\operatorname{r}\left(\begin{array}{ll}\boldsymbol{A}^{\mathrm{T}} & \boldsymbol{B}^{\mathrm{T}}\end{array}\right)$ ．
E
F