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