Red planetary looking object sighted near full moon in eastern sky above Pullman, WA

was just getting out of seeing a play a the Pullman Civic Theater and looked at the full moon.  Just below and to the right of the moon was what appeared to be a planet (was stationary) and red.  
I asked my wife to get out a look at what I though was Mars.  Object/light was stationary.  
I asked my mother to look as well...she looked out the windshield  at the light.  
My wife and I continued to stand outside of our vehicle and look at it, when it began to move down from the position it was in, or possibly east.  It then began to fade in intensity and eventually disappeared.  
I was near the corner of NW Nye St and NW Stadium way looking east over the top of Dissmores IGA store