Roleplaying in the world of the Matrix (first movie - the ONLY movie). Reloaded does not exist. It never existed. It will never exist. The same goes for Revolutions. Likewise for any animated films you might have heard of, and any other derivative products. Characters are defined by one Stat: MATRIX.
Every time you test a skill, you roll one die for your skill. If you are doing anything remotely physical - and are in the Matrix - you may also roll another die for your Matrix stat. It's best to have a different coloured die for this, as you will be making these rolls all the time (in fact, almost always) and you need to be able to tell them apart easily. If your skill roll or your Matrix roll succeeds, you have succeeded at your task. However, a Matrix success is always better than a skill success, in terms of game effect. If both rolls succeed, hey, you're a complete bad-ass, and you and the GM should work out an outcome to demonstrate that.