设 $\boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}$ 是三个 $n$ 阶方阵， $\boldsymbol{A B}=\boldsymbol{O}, \boldsymbol{A}+\boldsymbol{B C}=\boldsymbol{E}_n$ ．则有
A. $r(\boldsymbol{A})+r(\boldsymbol{B})=n$ ．
B. $r(\boldsymbol{A})+r(\boldsymbol{B})>n$ ．
C. $r(\boldsymbol{A})+r(\boldsymbol{B}) \leqslant 2 n$ ．
D. $r(\boldsymbol{A})+r(\boldsymbol{B}) < n$ ．