If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate lim (A^k)(B^k) as k approaches infinity.
You would probably be expected to exploit the properties of those non-negative primitive matrices which P-F can be applied to. I'd start by working though the definitions - bearing in mind what you understand about matrix manipulations. Note: there is a fair amount of overlap between the three conditions:
i.e.
is it possible to have a primitive matrix that is not non-negative?
what sorts of matrices can F-P be applied to?