Stationary Distribution of a Two-State Chain

Level 5●●○○○ Easy~4 min

Problem

A Markov chain has two states. From state 1 it moves to state 2 with probability aa; from state 2 it moves to state 1 with probability bb (with a,b(0,1)a,b\in(0,1)). Find the stationary distribution. How fast does the chain converge to it?
12ab1−a1−b

A two-state chain: 1→2 with probability a, 2→1 with probability b.