Let $\{X_n\}$, $n \geq 0$ be a Markov chain with the transition matrix $P$ such that $$ \begin{array}{c|ccc} &A &B &C \\ \hline A &0.2 & 0.2 &0.6\\ B &0 & 0.25 &0.75\\ C &0.3 & 0.3 & 0.4 \end{array}. $$
a) How to find all the stationary distributions?
b) If the Markov Chain starts in state $A$, what is the expected number of steps before it returns to $A$?
c) How many times, on average, does the Markov Chain visit state $B$ between two visits to $A$.
I'm finding this topic quite tricky, so I really appreciate the help you guys are giving me :) I'd love if someone could explain all the steps to me.. :)