2 A (left) stochastic matrix is one which has only non-negative (0) entries, and such that the entries in each column sum to 1. Let A be any (that is, a general) 2×2 stochastic matrix. (a) Show that one of the eigenvalues of A is 1. (b) Show that a general nxn stochastic matrix also has one eigenvalue equal to 1. (c) What happens if the column sums are 1, as above, but the entries may be any (possibly negative) real numbers. Hint Consider adding all the rows together.

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