It's possible to run an amplifier with a power inverter, but it's not always recommended and requires careful consideration. Finding the right power inverter to convert 12V DC to 220V AC is essential for powering electronics from a vehicle or off-grid solar source. This guide covers top 5 reliable inverters, each with unique features suited for cars, campers, RVs, and emergency power. Inverter itself is not a problem, I could get 1500W continuous (2500W peak) 12V/220V inverter relatively cheaply (£80). However, based on what I have seen car simply can't supply enough. Check each product page for other buying options. Price and other details may vary based on product size and color. For a 2000 watt inverter 200 amp discharge rate would be minimum battery rating and closer to. Not sure about your amp's PSU, but I believe it outputs +-X volts, you could power it directly from car SMPS like 12V -> +-X volts. i intend to step up to say 6KHz.
[PDF Version]