If matrices A and B commute, then the formula A2B = BA2 must hold.
The statement is true.
The claim is that if A and B commute then . First by definition if A and B commute this means that thus we will have:
Thus the statement is true.
In this exercise we will verify part (b) of Theorem 2.3.11 in the special case when A is the transition matrix is the distribution vector . [We will not be using parts (a) and (c) of Theorem 2.3.11]. The general proof of Theorem 2.3.11 runs along similar lines, as we will see in Chapter 7.
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