（武汉大学，2013 年）设 $A=\left(\begin{array}{lll}1 & 2 & 2 \\ 2 & 5 & 4 \\ 2 & 4 & 5\end{array}\right), B=\left(\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right), C=\left(\begin{array}{lllll}1 & 1 & & & \\ & 1 & 1 & & \\ & & 1 & 1 & \\ & & & 1 & 1 \\ & & & & 1\end{array}\right)$ ，求矩阵 $\boldsymbol{X}$ 使 $\boldsymbol{X}\left(\begin{array}{ll}\boldsymbol{O} & \boldsymbol{B} \\ \boldsymbol{A} & \boldsymbol{O}\end{array}\right)=\boldsymbol{C}$ ．