The Matrix received the same AWD system used on the ST215 Auto Caldina wagons known as "V-Flex" and isn't the same as the alltrac.
V-Flex is a lazy 4WD system and only occasionally partially locks up and kicks in when slipping or cornering because power is sent into the front diff first.
They don't really have a center differential and most of the transfercase assy is in the rear diff.https://www.youtube.com/watch?v=yMwAysEHRYQ
Note how the fronts are able to spin when the rears don't and the engine doesn't stall from resistance. In an alltrac all four wheels would be spinning if the car was beached on snow however if two wheels are stuck/slipping you'll stall the engine from the resistance in the drivetrain.
Would be interesting if you could fit the FWD Matrix front LSD and lock the center of the AWD model though... not too sure if you'd want to street that setup however!