A Markov Process for Two States Has the Following Transition $$\begin{array} { c c c } & \mathrm { A } & \mathrm { B } \\\text { A } & 0.35 & 0.65 \\\text { B } & 0.42 & 0.58\end{array}$$

Short Answer

A Markov process for two states has the following transition matrix:
$$\begin{array} { c c c } & \mathrm { A } & \mathrm { B } \\\text { A } & 0.35 & 0.65 \\\text { B } & 0.42 & 0.58\end{array}$$
Assume that we start with state 1, what is the probability matrix of the system being in state A or B in period 3 given the system started in state B?