I've worked out my characteristic equation to be $\displaystyle \lambda^{3} - 4\lambda^{2} - 4\lambda + 16 = 0 $

I have been letting $\displaystyle p(\lambda) = \lambda^{3} - 4\lambda^{2} - 4\lambda + 16 $ and filling in values for $\displaystyle \lambda $ which are the factors of 16 i.e. $\displaystyle \lambda = 1,-1,2,-2,4,-4,8,-8,16,-16 $.

However this method cannot tell me if an the same eigenvalue occurs twice... which i've a feeling in this case occurs...

Any thoughts?