Here are the weapons we can see him using:
* M60 Machine Gun: This is the main weapon Matrix uses throughout the film, both on the island and in the city.
* Thompson Submachine Gun: He briefly uses this during the island escape sequence.
* M1911A1 Pistol: Matrix carries this as his sidearm.
* M79 Grenade Launcher: Used in a few scenes, notably when he takes out the helicopter.
* M203 Grenade Launcher: This is attached to his M16 rifle for grenade launching.
* M16A1 Rifle: Matrix uses this during the climactic showdown.
* Hand Grenades: He utilizes these on multiple occasions.
There are a few other weapons seen in the film, but Matrix doesn't use them himself. For example, the villain Bennett uses a Uzi submachine gun, and there are a few other weapons seen on the island, but Matrix doesn't use them.
If you are looking for the specific names of every single weapon used on the island, that would be a very detailed analysis of the movie!