9. Prove that if the number of states in a Markov chain is M, and if state j can be reached from state /, then it can be reached in M steps or less.

*10. Show that if state / is recurrent and state i does not communicate with statey, then Pu = 0. This implies that once a process enters a recurrent class of states it can never leave that class. For this reason, a recurrent class is often referred to as a closed class.