设 $A=\left(\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right), B=\left(\begin{array}{cc}a_{21}+a_{11} & a_{22}+a_{12} \\ a_{11} & a_{12}\end{array}\right), P_1=\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right), P_2=\left(\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right)$, 则