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\begin{document}
\begin{equation*}
  \begin{bmatrix} -1 & {\color{blue} f'_1} \\ {\color{blue} f'_2} & -1 \end{bmatrix}
  \begin{bmatrix} p_{11} & p_{12} \\ p_{12} & p_{22} \end{bmatrix} + 
  \begin{bmatrix} p_{11} & p_{12} \\ p_{12} & p_{22} \end{bmatrix}
  \begin{bmatrix} -1 & {\color{blue} f_2'} \\ {\color{blue} f'_1} & -1 \end{bmatrix} =
  \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix},
\end{equation*}
\end{document}