A is the matrix $\displaystyle \begin{bmatrix} 2 & 2 & -2 \\ 2 & -1 & 4\\ -2 & 4 & -1 \end{bmatrix}$. You are given that A has eigenvalues -6 and 3, with algebaric multiplicities 1 and 2 respectively, and that the eigenspace $\displaystyle V_{3} = span{(2,-1,-2),(2,2,1)} $.

a) use the given eigenvalues to find the characteristic equation of A. (do not expand det(A-ILAMBDA), but the construct the equation from its roots.

Hence use the hamilton theorem to find A^{-1} .

I dont know where to being. Any help appreciated,