Most Mosfets turn on when their gate is 10V or a little more higher than their source voltage. They turn off when their gate voltage is the same as their source voltage. For a low frequency square-wave inverter two Mosfets can be driven by a CD4047 Cmos oscillator. For high frequency pulse-width-modulation for motor speed control then a Mosfet driver IC should be used to quickly charge and discharge the high gate capacitance of the Mosfets, and to provide dead-time so that one Mosfet is off when the other turns on.
A 2000W square-wave inverter will dissipate about 400W of heat. It will draw 200A continuously from a 12V battery at full load which will cause it to explode. You will need many output transistors, a huge and expensive custom-made transformer and a bus full of car batteries that will take a week to charge. Rediculous.
Some 2000W inverters operate from 48VDC then four car batteries in series last a few hours.
Any inverter will last for 2 hours or more if its battery is big and its load current is low. I can buy a amall 75W inverter for a low price. A car battery will last 10 hours powering it if it has a 75W load.
The current in the output transistors and from the battery will be 150A if the load on a 12V inverter is 1500W. A big car battery will explode. The transformer will be huge and will cost a fortune. Many transistirs will be needed. Rediculous.