Probability that Markov chain process has particular state after n steps

Question

If we have a Markov chain X with four discrete states, and we want to find the probability the process is in a certain state (one of the four) n iterations later, would we raise X to the nth power and locate the value of the appropriate corresponding matrix element (i.e. 1,4 if the process starts in state one, and ends in state 4) to find this probability?

Answer 1

Yes, that's exactly how we'd do it.