# Math Help - Eigenvalues for 3x3 Matrix

1. ## Eigenvalues for 3x3 Matrix

Trying to find eigenvalues for this matrix $A - \lambda I$

$\left(\begin{array}{ccc}{1 - \lambda} & 2 & {-2} \\ 2 & {1 - \lambda} & 0 \\ {-2} & 0 & {1 - \lambda} \end {array} \right)$

If my math is correct, the determinant of this is ${(1-\lambda)}^3 - 8\lambda - 12$, but this doesn't factor, so I don't know how to find the roots.

Can somebody help? Thanks.