back window wont roll up

The first thing I would check is the fuses. For this, they’re usually in the car on the driver's side. Refer to the fuse guide on the cover and verify it with a multimeter. If you don't own a multimeter, gett a $50-100 auto-range True RMS multimeter, such as a Klein like this: https://www.lowes.com/pd/Klein-Tools-Dig... ($60, 4,000 count) or this: https://www.lowes.com/pd/Klein-Tools-Dig... ($100, 6,000 count).

If you do not intend to use it beyond DC work, a relatively inexpensive Cat III from a place like Harbor Freight is an option. Try to get one with Cat III, Cat II and older should be avoided. This one is lacking TRMS which means it will be prone to inaccuracies on non-linear circuits, but it is cheap at $40 (and you can probably use a coupon to get it down more): https://www.harborfreight.com/electrical...

If you do not see any bad fuses, then the next step I would take is to check the wiring on the car where the switch is and verify that the harness is receiving power. If you see 12V on the harness connected to the chassis, then we know the car is receiving power. You can usually remove this from most GM products from this era by removing one screw, but some have tabs that are easily broken. In this case, you need to use extreme care or remove the door card and dislodge them from the inside to avoid damage.

This is for the 2008 year, so it should be the same for 2008-2012, but if you want an exact diagram, search: (model year) Chevy Malibu electrical diagram: https://www.scribd.com/document/71455532...

If you want to be absolutely sure that the regulator is faulty, use a 9V battery or a 12V SLA battery, such as those found in a UPS or a car, and then determine the polarity (again, using the DMM). if it says -0V means you reversed the polarity (and know which one is negative), 0V means it is positive to negative, and you found the positive. Take note of the pinout and connect a battery to it directly with the door card removed for easy access. If the regulator moves with nothing else connected, the door panel switch is broken. Both are very common faults in GM vehicles. If it gets power, the door card switch is broken - not the regulator.

If you’ve checked both of these and it isn't off track, where you can remove the door card to reseat the window, then the regulator is bad. At that point, without a model number, we’re stuck, but if you search (Model year) Chevy Malibu (bad) window regulator. At that point, I would also look for a matched year service manual to make sure you have the correct procedure for your car, as it can change slightly between years.