已知 $P _1=\left(\begin{array}{llll}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right), P _2=\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right), B =\left(\begin{array}{llll}0 & 0 & 0 & 1 \\ 0 & 0 & 2 & 0 \\ 2 & 3 & 0 & 0 \\ 3 & 5 & 0 & 0\end{array}\right)$ 满足 $\left( P _1^{-1}\right)^5 A \left( P _2^{-1}\right)^2= B$ ，则 $A ^*=$