I have been trying to compute the cokernels of powers of integer matrices using Smith normal form.
When is $\text{Smith}(A^2) = (\text{Smith}(A))^2$ and more generally when is $\text{Smith}(A^n) = (\text{Smith}(A))^n$?
Some numerical experiments showed that this is not always true. Is there at least a good sufficient condition for determining when such a formula holds? Thanks!