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regular markov chains

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Suppose a gene in a chromosome is of type A or type B. Assume that the probability that a gene of type A will mutate to type B in one generation is 10^-4 and that a gene of type B will mutate to type A is 10^-6.

(A) What is the transition matrix?
(B) After how many generations, what is the probability that the gene will be of type A? of Type B? (Find the stationary matrix)

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Markov Chain: Invariant Distribution

Please see attached file.

Consider the Markov chain with transition matrix (please see the attached file) where 0 <= p <= 1 and 0 <= q <= 1. Find an invariant distribution of this chain, For which values of p and q is the distribution unique? Given an initial distribution (please see the attached file), for which values of p and q will this distribution evolve toward the unique invariant distribution?

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