设 $A=\left(\begin{array}{ccc}1 & 0 & -1 \\ 2 & a & 1 \\ 1 & 2 & 1\end{array}\right)$, 且 $r(B)=2, r(A B)=1$, 则
$\text{A.}$ $r\left(\left(\begin{array}{ll}A^* & O \\ A & B\end{array}\right)\right)=3$
$\text{B.}$ $r\left(\left(\begin{array}{ll}A & O \\ O & B^*\end{array}\right)\right)=3$
$\text{C.}$ $r\left(\left(\begin{array}{cc}A^* & B \\ O & B^*\end{array}\right)\right)=3$
$\text{D.}$ $r\left(\left(\begin{array}{ll}A & B^* \\ O & B\end{array}\right)\right)=3$