Say that I have a finite Markov chain, which has transition matrix P. Assume P is an nxn matrix.

Then, define K(n) as the smallest integer n such that P will be a "regular" matrix iff P^n > 0.

Find K(3) by checking all of the cases.

Now, I'm not looking for a solution or descriptions of how to complete this problem ... I'm just clueless as to what this is actually asking for. Could someone please explain what this question wants, without actually solving it for me?

Thanks much!