Your not going to run a fridge off a couple batteries very long. Remember that power into the inverter has to equal power out of the inverter. So your 120v 10A fridge is 1200w, taking 1200w on the input side divided by 12v your drawing 100A. Then if your inverter doesn't have an energy star label its less than 80% efficient so your loosing at least 20% to inversion loss which means 120A draw from the batteries.
Granted that 10A probably isn't the continuous running current but its still a lot.