Diagonalize the following matrix if possible.
A=
|4 , 2 , 2|
|2 , 4 , 2|
|-2, 2 , 4|
Help for some starters?
pickslide's question was "do you know how to find eigenvectors", not eigenvalues!
A 3 by 3 matrix can be diagonalized if and only if it has 3 independent eigenvectors.
If that is true then $\displaystyle P^{-1}AP$ is diagonal where P is the matrix having A's eigenvectors as columns.