Inverter conversion to 120 volt alternating current is extraordinarily inefficient
Let's frame that statement with a qualifier - that solar electricity conversion is inefficient.
Imagine a square meter surface area facing the sun may see 700 to 1000 watts energy during each of the 5 peak sun-hours each day.
If you are collecting that as heat transferred into water, a collector may see over 70% efficiency in harvesting the sunlight, and the complete system may hold up to 30 or 35% efficiency... or, a square meter of panel may harvest 350 watts of usable heat energy per hour.
If you are collecting that sunlight as electricity the PV collectors may see 12-18% conversion and the losses from batteries, wiring and inverter (not counting the ultimate load) drop that to 7 to 11%. So a square meter of PV collector may harvest 70 to 110 watts of usable electric energy per hour.
Now factor in clouds - days long weather events - and all the hassles of locating the panels for optimum performance - and our $$$ investments efficiency drops yet again. See Surface meteorology and Solar Energy
for your local site data.
The greatest gain anyone can see is through conservation - limiting the need in the first place - which is really what building 'green' is all about...