Write a code that takes a N times N transition probability matrix and a positive number n, and produces the n-th power of a transition probability matrix, presenting the output in visual form (i.e. writing the rows and columns of the matrix). Use this to calculate p^2, p^5, p^10, p^20 and p^40 for: the Gambler's ruin (with M = 4), the Ehrenfest chain (with N = 4), and the Wright-Fisher model (with N = 4). For each matrix, what pattern do you see as n increases