设
$$
\boldsymbol{A}=\left(\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{array}\right), \quad \boldsymbol{B}=\left(\begin{array}{ccc}
a_{21} & a_{22} & a_{23} \\
a_{11} & a_{12} & a_{13} \\
a_{31}+a_{11} & a_{32}+a_{12} & a_{33}+a_{13}
\end{array}\right),
$$
$$
\boldsymbol{P}_{1}=\left(\begin{array}{lll}
0 & 1 & 0 \\
1 & 0 & 0 \\
0 & 0 & 1
\end{array}\right), \quad \boldsymbol{P}_{2}=\left(\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 1
\end{array}\right),
$$
则必有 ( )
A. $\boldsymbol{A} \boldsymbol{P}_{2} \boldsymbol{P}_{1}=\boldsymbol{B}$.
B. $\boldsymbol{A P} \boldsymbol{P}_{1}=\boldsymbol{B}$.
C. $\boldsymbol{P}_{2} \boldsymbol{P}_{1} \boldsymbol{A}=\boldsymbol{B}$.
D. $\boldsymbol{P}_{1} \boldsymbol{P}_{2} \boldsymbol{A}=\boldsymbol{B}$.