\[ \text{If A = } \begin{bmatrix} 2&1&1 \\ 1& 2 & 1 \\ 1 &1& 2 \end{bmatrix} \] \[ \text{verify that } A^{3} - 6A^{2} + 9A - 4 I = O. \text{ Hence, find } A^{-1}\]

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