设$$
\begin{gathered}
\mathbf{A}=\left(\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{array}\right), \quad \mathbf{B}=\left(\begin{array}{ccc}
a_{21} & a_{22} & a_{23} \\
a_{11} & a_{12} & a_{13} \\
a_{31}+a_{11} & a_{32}+a_{12} & a_{33}+a_{13}
\end{array}\right), \\
\mathbf{P}_1=\left(\begin{array}{lll}
0 & 1 & 0 \\
1 & 0 & 0 \\
0 & 0 & 1
\end{array}\right), \quad \mathbf{P}_2=\left(\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 1
\end{array}\right),
\end{gathered}
$$
则必有
$\text{A.}$ $\mathbf{A} \mathbf{P}_1 \mathbf{P}_2=\mathbf{B}$;
$\text{B.}$ $\mathbf{A P}_2 \mathbf{P}_1=\mathbf{B}$;
$\text{C.}$ $\mathbf{P}_1 \mathbf{P}_2 \mathbf{A}=\mathbf{B}$;
$\text{D.}$ $\mathbf{P}_2 \mathbf{P}_1 \mathbf{A}=\mathbf{B}$.