Can a permanent resident travel to and back from mexico, with there mexico passport and resident card?

Or do they need to become u.s citizens? then get there passport. ????

As a permanent resident of the U.S., you certsinly may travel to and from Mexico with your Mexican passport and permaent resident card...that is exactly the right thing to do. be sure you always keep your Mexican passport current until the time you become a U.S. citizen and can get a U.S. passport.

Charlie is totally right