Consider the following transition probability matrix:

You are required to (i) provide an example of path in this;
(ii) give an example of states which communicate;
(iii) provide an example of recurrent state;
(iv) provide an example of transient state; and (v) identify if there exists an absorbing state.

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0.3 0.7 0 0 0 0.5 0.5 0 0 0 P = 0 0 0 0.8 0.2 0 0 0 0.4 0.3 0.3 0 00 0 0 0.1 0.1 0.9