设 $n$ 阶实对称矩阵 $\mathbf{A}, \mathbf{B}$ 均可逆，则下列说法中，正确的是
A. 矩阵 $\left(\begin{array}{cc}\mathbf{E} & \mathbf{B A} \\ \mathbf{A B} & \mathbf{O}\end{array}\right)$ 与 $\left(\begin{array}{ll}\mathbf{E} & \mathbf{O} \\ \mathbf{O} & \mathbf{O}\end{array}\right)$ 合同．
B. 矩阵 $\left(\begin{array}{cc}\mathbf{E} & \mathbf{B A} \\ \mathbf{A B} & \mathbf{O}\end{array}\right)$ 与 $\left(\begin{array}{ll}\mathbf{E} & \mathbf{O} \\ \mathbf{O} & \mathbf{E}\end{array}\right)$ 合同．
C. 矩阵 $\left(\begin{array}{cc}\mathbf{E} & \mathbf{B A} \\ \mathbf{A B} & -\mathbf{E}\end{array}\right)$ 与 $\left(\begin{array}{ll}\mathbf{E} & \mathbf{O} \\ \mathbf{O} & \mathbf{E}\end{array}\right)$ 合同．
D. 矩阵 $\left(\begin{array}{cc}\mathbf{E} & \mathbf{B A} \\ \mathbf{A B} & -\mathbf{E}\end{array}\right)$ 与 $\left(\begin{array}{cc}\mathbf{E} & \mathbf{O} \\ \mathbf{O} & -\mathbf{E}\end{array}\right)$ 合同．