Please read my post again where I explain about the total capicity of the batteries, he can not store 3kw in 2*100ah, a battery can only store volt*amps so 12v*100A = 1200w MAX per battery, and that is not even always possible, charging the last 10% takes forever and the battery ages it becomes impossible to hold 100%.

But eitherway the best case scenario is 1200w per battery so 2400w per battery even if he uses a billion solar panels.

Also the inverter loss is not everything, there is still charging loss and transmission loss, unless you use the highest quality of everything it is safe to assume a 20% in the whole system.