I completed the other half of the exercise now. So two exercises are now done.

I have now completed the second half of a problem concerning communicating classes of a markov chain transition probability matrix. What we do is this: "For state we evaluate for all . and any and at the same time evaluate for any . If we can show that for any and also that for any we have shown that the states and communicate. This allows us to establish which states communicate and then grouping all states by ability to communicate allows us to establish the different classes of states.