Chapter 9.1, Problem 72E

In Problems 71-74, given the transition matrix $P$ and initial-state matrix $S_0$, find $P^4$ and use $P^4$ to find $S_4$.

$\begin{array}{l}\begin{array}{cc}A& B\end{array}\\ P=\begin{array}{c}A\\ B\end{array}\left[\begin{array}{cc}.8& .2\\ .3& .7\end{array}\right];S_0=\left[\begin{array}{cc}.4& .6\end{array}\right]\end{array}$