We are given

P = 1/2 1/4 1/4 0 1 0 1/2 1/2 0 .

This is the one-step transition matrix. The two-step transition matrix is given by P²:

P2 = P P = 1/2 1/4 1/4 0 1 0 1/2 1/2 0 1/2 1/4 1/4 0 1 0 1/2 1/2 0 = 3/8 1/2 1/8 0 1 0 1/4 5/8 1/8 .

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