设 A 为 m 阶可逆矩阵， B 为 n 阶可逆矩阵，则可逆分块矩阵 $D=\left(\begin{array}{ll}O & A \\ B & O\end{array}\right)$ 的逆矩阵是
A. $\left(\begin{array}{cc}A^{-1} & O \\ O & B^{-1}\end{array}\right)$
B. $\left(\begin{array}{cc}O & B^{-1} \\ A^{-1} & O\end{array}\right)$
C. $\left(\begin{array}{cc}B^{-1} & O \\ O & A^{-1}\end{array}\right)$
D. $\left(\begin{array}{cc}O & A^{-1} \\ B^{-1} & O\end{array}\right)$