Please help i am so lost
Let P be the transition matrix of a finite Markov chain (with n states) such that the column and rows sums to 1. Show that the stationary distribution for this Markov chain has all states equally probable. Deduce that if the Markov chain is ergodic, then the mean number of transitions
taken to return to each state is the same as the total number of states, n.
What is "the" stationary distribution when the Markov chain is periodic, or reducible with more than one closed classes?