$A, B$ 分别是 $m$ 阶和 $n$ 阶方阵, 则 $\left[\begin{array}{ll}O & A \\ B & O\end{array}\right]$ 的伴随矩阵是
A. $\left[\begin{array}{cc}O & |B| B^* \\ |A| A^* & O\end{array}\right]$
B. $(-1)^{m n}\left[\begin{array}{cc}O & |A| B^* \\ |B| A^* & O\end{array}\right]$
C. $(-1)^{m n}|A||B|\left[\begin{array}{cc}O & B^{-1} \\ A^{-1} & O\end{array}\right]$
D. $(-1)^{m n}|A||B|\left[\begin{array}{cc}O & B^* \\ A^* & O\end{array}\right]$