Chapter 9.1, Problem 61E

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

$\begin{array}{l}\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}0& .4& .6\\ 0& 0& 1\\ 1& 0& 0\end{array}\right];S_0=\left[\begin{array}{ccc}.2& .3& .5\end{array}\right]\end{array}$