设 $A 、 B$ 为 $n$ 阶实对称, 下列不成立的是（ )
$\text{A.}$ $r\left(\begin{array}{cc}A & O \\ O & A A^{T}\end{array}\right)=2 r(A)$.
$\text{B.}$ $r\left(\begin{array}{cc}A & A B \\ O & A^{T}\end{array}\right)=2 r(A)$.
$\text{C.}$ $r\left(\begin{array}{ll}A & B A \\ O & A A^{T}\end{array}\right)=2 r(A)$.
$\text{D.}$ $r\left(\begin{array}{cc}A & O \\ B A & A^{T}\end{array}\right)=2 r(A)$.