$\mathrm{A}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right];\mathrm{I}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ and ${\mathrm{A}}^{-1}=\left[\frac{1}{6}({\mathrm{A}}^2+\mathrm{CA}+\mathrm{DI})\right].$ The values of C and D are

$\begin{array}{rcl}\mathrm{A}& =& \left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right]\\ \mathrm{trace}\left(\mathrm{A}\right)& =& 1+1+4=6\end{array}$

Sum of Minor of Principle diagonal

$$\begin{gathered} =\left|\begin{array}{cc}1& 1\\ -2& 4\end{array}\right|+\left|\begin{array}{cc}1& 0\\ 0& 4\end{array}\right|+\left|\begin{array}{cc}1& 0\\ 0& 1\end{array}\right| \\ =4+2+4+1=11 \\ \left|\mathrm{A}\right|=1 (4+2)=6 \\ {\mathrm{A}}^3-6{\mathrm{A}}^2+11\mathrm{A}-6\mathrm{I}=0 \\ {\mathrm{A}}^{-1} \left({\mathrm{A}}^3-6{\mathrm{A}}^2+11\mathrm{A}-6\mathrm{I}\right)=0 \\ {\mathrm{A}}^{-1} \mathrm{A} {\mathrm{A}}^2-6{\mathrm{A}}^{-1} \mathrm{A} \mathrm{A}+11{\mathrm{A}}^{-1} \mathrm{A}-6{\mathrm{A}}^{-1} \mathrm{I}=0 \\ \mathrm{I} {\mathrm{A}}^2-6\mathrm{IA}+11\mathrm{I}-6{\mathrm{A}}^{-1}=0 \\ 6{\mathrm{A}}^{-1}={\mathrm{A}}^2-6\mathrm{A}+11\mathrm{I} \\ {\mathrm{A}}^{-1}=\frac{1}{6} \left({\mathrm{A}}^2-6\mathrm{A}+11 \mathrm{I}\right) \\ \mathrm{C}=-6, \mathrm{D}=11 \\ (\mathrm{C}, \mathrm{D})=(-6, 11) \end{gathered}$$