2. (a) Let A = 0 0 2 0 0 1 200 0 0 7 0 0 00 0 9 20 4 0 0 1 0 Is A reducible? Justify your answer. (b) Let A be a nonnegative matrix such that its spectral radius is positive and there is an associated positive eigenvector. Should A be irreducible? Justify with a proof or provide a counter example.

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