Mad Matrix can be accessed through completing the Hero Mission on Prison Island, or the Normal Mission on Circus Park. Mad Matrix has a Hero, Normal, and Evil Mission.
The storyline of Mad Matrix:
Vector the Crocodile, Espio the Chameleon, and Charmy Bee, a.k.a. Team Chaotix, are standing around a computer. A large machine is in front of them. Vector begins complaining about how long Esipio's taking to hack Eggman's computer. Then, Charmy begins saying, "Can I try? I wanna try, I wanny try!" They hear the door open and they all jump up. Espio says, "An assassan?" It's really just Shadow. Shadow finds that they wanted to hack into Eggman's computer as well. He then karate chops the computer and the portal into cyberspace is opened. As the Chaotix stare in awe, Shadow jumps through. Espio goes in after him.
You must help Espio collect data from the four terminals around the area. The first one is at the very beginning. After you collect that, you must go to each of the four towers (red, green, yellow, and, blue) and collect data from every one.
You must find the exit from the matrix. The exit is inside the red tower. if you have Espio with you, he will say, "What the... Who put this here?" When you enter the last room. The exit is atop the large, purple sphere in the center.
You must help Doom's Eye detonate all of the bombs. They all lie within the large field between the four towers. They aren't hard to find.