Chapter 9.3, Problem 2MP

Use a transition diagram to determine whether $P$ is the transition matrix for an absorbing Markov chain.

$\begin{array}{l}\left(\text{A}\right)\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}.5& 0& .5\\ 0& 1& 0\\ 0& .5& .5\end{array}\right]\end{array}$

$\begin{array}{l}\left(\text{B}\right)\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right]\end{array}$