Write a code that takes a N 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)

(a) Use this to calculate p², p⁵, p¹⁰, p²⁰ and p⁴⁰ for: the Gamblers ruin (with M = 5) and the Ehrenfest chain (with N = 6).

(b) What pattern do you see as n increases for each matrix?