Determinants

If \(A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix}\), verify that \(A^3 - 6A^2 + 9A - 4I = O\) and hence find \(A^{-1}\).