设 $A, B$ 为 $n$ 阶矩阵， $A^*, B^*$ 分别为 $A, B$ 对应的伴随矩阵，分块矩阵 $C=\left(\begin{array}{cc}A & 0 \\ 0 & B\end{array}\right)$, 则 $C$ 的伴随矩阵 $C^*=(\quad)$
$\text{A.}$ $\left(\begin{array}{cc}|A| A^* & 0 \\ 0 & |B| B^*\end{array}\right)$
$\text{B.}$ $\left(\begin{array}{cc}|B| B^* & 0 \\ 0 & |A| A^*\end{array}\right)$
$\text{C.}$ $\left(\begin{array}{cc}|A| B^* & 0 \\ 0 & |B| A^*\end{array}\right)$
$\text{D.}$ $\left(\begin{array}{cc}|B| A^* & 0 \\ 0 & |A| B^*\end{array}\right)$