\documentclass[12pt]{article}
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\usepackage{color}
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\begin{document}
\begin{equation*}
  \begin{bmatrix} 
    -2 p_{11} + 2 {\color{blue} f'_1} p_{12} & p_{11} {\color{blue} f'_2} - 2 p_{12} + p_{22} {\color{blue} f'_1} \\
    p_{11} {\color{blue} f'_2} - 2 p_{12} + p_{22} {\color{blue} f'_1} & -2 p_{22} + 2 {\color{blue} f'_2} p_{12}
  \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix},
\end{equation*}
\end{document}