设 $A, B$ 为 $n$ 阶可逆矩阵， $E$ 为 $n$ 阶单位矩阵， $M^*$ 为 $M$ 的伴随矩阵，则 $\left(\begin{array}{ll}A & E \\ O & B\end{array}\right)^*=(\quad)$
A. $\left(\begin{array}{cc}|A| B^* & -B^* A^* \\ O & |B| A^*\end{array}\right)$
B. $\left(\begin{array}{cc}|A| B^* & -A^* B^* \\ O & |B| A^*\end{array}\right)$
C. $\left(\begin{array}{cc}|B| A^* & -B^* A^* \\ O & |A| B^*\end{array}\right)$
D. $\left(\begin{array}{cc}|B| A^* & -A^* B^* \\ O & |\boldsymbol{A}| B^*\end{array}\right)$