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\begin{document}
\begin{equation*}
  \aligned 
    G_{yu}(s) &= C (sI - A)^{-1} B = \begin{bmatrix} 1 & 0 \end{bmatrix}
      \begin{bmatrix} s & -\omega_0 \\ \omega_0 & s + 2 \zeta\omega_0 \end{bmatrix}^{-1}
      \begin{bmatrix} 0 \\ k \omega_0 \end{bmatrix} \\
    &= \begin{bmatrix} 1 & 0 \end{bmatrix} \left( \frac{1}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}
      {\color{blue} \begin{bmatrix} s + 2 \zeta\omega_0 & -\omega_0 \\ \omega_0 & s \end{bmatrix}} \right)
      \begin{bmatrix} 0 \\ k \omega_0 \end{bmatrix} \\ & = \frac{k \omega_0^2}{s^2 + 2 \zeta\omega_0 s +
        \omega_0^2}
 \endaligned
\end{equation*}
\end{document}