Yes. Not required but generally a good idea to reduce the chance of creating a ground loop. And yes, you do the same thing for negative as you do for positive. For example, in my car I ran 2 gauge + and - to the trunk from the battery. Then in the trunk, I made a common ground for the entire system. So every component in my system is grounded to that point including the stereo. Keep in mind that with amplifiers that you are amplifying any noise in the system, so it becomes more important. I hope that helps.