a housekeeper buys three kinds of cereal; A,B,C. She never buys the same cereal in successive weeks. if she buys cereal A, then the next week she buys cereal B. However, if she buys either B or C, then the next week she is three times as likely to buy A as the other brand.
a) find the transition matrix
b) in the long run, how often does she buy each of the three brands?
for a. i got
[0 1 0]
|.6 0 .2|
[.6 .2 0]
im not sure how to do the second part or if i got the right transition matrix for part a. help?