Find the inverse: \(\begin{bmatrix}1 & 2 & 2 \\ 1 & 2 & -1 \\ -1 & 1 & 4\end{bmatrix}\)

\(\begin{bmatrix}1 & \dfrac{-2}{3} & \dfrac{-2}{3} \\[0.75em]
\dfrac{-1}{3} & \dfrac{2}{3} & \dfrac{1}{3} \\[0.75em]
\dfrac{1}{3} & \dfrac{-1}{3} & 0
\end{bmatrix}\)