Take various stochastic matrices with random entries, raise them to higher and higher powers, and observe the results.
Make a conjecture about the limiting form of the matrix powers. Before making TOO strong a conjecture consider the rather special (non-random) case of the stochastic matrix with first row [0 1] and second row [1 0].
The result aimed at here is nontrivial. Discuss your conjecture with your instructor and/or consult a book that discusses the topic of MARKOV CHAINS.