Exchange front wheel with rear wheel (Matrix 750) on Trek 4500 mountain bike? My rear wheel has been showing around the rim some wear on one side. Perhaps something to do with my braking.

I was wondering if I can exchange the front wheel with the rear one (in other words, can the gear sprockets be uninstalled and put on the other wheel)? My bicycle is a Trek 4500 (and the wheels say Matrix 750 on them). 

If the above is not plausible then can the rear wheel be flipped (that is, the side be changed), again with the gear sprockets being replaced and placed appropriately?
No, not possible. 

Front wheels are front wheels and back wheels are back wheels. 

The gears are a cassette of cogs that slide onto the freehub which is the bit that lets you go forward when pedalling and coast when not. You can’t flip a back wheel in the drop outs. 

“Some wear” is normal on a trail bike with rim brakes, but your local bike store will be able tell if it’s too far gone and advise you if you need a new rim or possibly more economical a new wheel. However rims are very durable and should last at least a few years even with grindy winter mud sessions.

Also the spec claims the hubs are disk ready. If that’s true and you can afford to spend a little money you may be able to upgrade to disk brakes. 

Ask a bike mechanic first.