We are given

P = 0.2 0.8 0.8 0.2 .

Now, the probability of going from state 2 to state 1 in two steps is given by the (2, 1) entry of the two-step transition matrix, P². We calculate

P2 = P.P = 0.68 0.32 0.32 0.68 .

Since the (2, 1) entry is 0.32, the probability of going from state 2 to state 1 in two steps is 0.32

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