The other day, we were out to work on a boat because the small battery bank was dying after 1-2 days at anchor even with nothing turned on. With everything on the boat turned off , there was a constant 1.5A draw on the house bank. It was traced to a 1000W inverter that was hardwired in a closet and always left on. Inverters are used to convert the DC power from your batteries to AC power for your outlets. Even with no AC loads, the inverter still used 1.5A of current in "standby". This is typical of inverters. The owner had no easy way of turning off the inverter. Every inverter should have an easy way of turning it off and on.
Typically a remote panel mounted near the main AC or DC panel allows you to turn it off when not needed. Some inverters, like the magnum MS series, have a power search mode and will stay in "sleep mode" if nothing is plugged in, and then will come awake if you plug a device in or turn on an AC load. This saves power (about .5A in search mode instead of 2A in standby on the MS2012) but still uses some. If you don't plan to use the inverter for hours or days at a time the best bet is to shut it off.