Examine the nature of the states of the Markov chain having transition probability matrix link
Here is my approach so far. link
What I did was follow the technique mentioned here. link
However, I quickly realised that this will get complex really fast due to the high number of combinations possible. Hence, I realised there had to be another way. I then learnt that
If i<->j and if i is recurrent then j is recurrent.
That seemed to make things easier. If I can prove one is recurrent, then I can prove they are all recurrent, as all the states communicate with one another. Except, that I am still unsure about how to prove that any of one these are recurrent states. How should I do this? If someone could nudge me in the right direction, I would really appreciate it. The questions that I have found thus far on Stack-Ex have not been able to make me understand what I have to do.