Chapter 9.2, Problem 33E

Problems 31-34 refer to the regular Markov chain with transition matrix

$P=\left[\begin{array}{cc}.5& .5\\ .2& .8\end{array}\right]$

For $S=\left[\begin{array}{cc}0& 0\end{array}\right]$, calculate $SP$. Is $S$ a stationary matrix? Explain.