已知矩阵 $A=\left(\begin{array}{ccc}1 & 0 & -1 \\ 2 & -1 & 1 \\ -1 & 2 & -5\end{array}\right)$ ，若下三角可逆矩阵 $P$ 和上三角可逆矩阵 $Q$ 使 $P A Q$ 为对角矩阵，则 $P, Q$ 可分别取为
A. $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right),\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right)$
B. $\left(\begin{array}{ccc}1 & 0 & 0 \\ 2 & -1 & 0 \\ -3 & 2 & 1\end{array}\right),\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)$
C. $\left(\begin{array}{ccc}1 & 0 & 0 \\ 2 & -1 & 0 \\ -3 & 2 & 1\end{array}\right),\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{array}\right)$
D. $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 1\end{array}\right),\left(\begin{array}{ccc}1 & 2 & -3 \\ 0 & -1 & 2 \\ 0 & 0 & 1\end{array}\right)$