[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]\mat{P}[/math] be the transition matrix of an ergodic

Markov chain and [math]\mat{P}^*[/math] the reverse transition matrix. Show that they have the same fixed probability vector [math]\mat{w}[/math].