Can the US be powered by a 100 x 100 miles solar grid?
Desertec is basically the same idea, solar plants located in North Africa supplying power to Europe. The article includes a map showing the area required to power Germany, Europe, and the whole world, respectively, as estimated by the German Aerospace Center (DLR). That estimate puts 100x100 miles for the USA in the "plausible" ballpark.
Why didn't anyone built this square already?
This isn't part of the claim by Elon Musk, but some thoughts on this:
One, solar power is dependant on sunlight (obviously). Your solar plant would produce power only at daytime, and at limited capacity when it's overcast. You would need to build excess capacity to cater for bad weather, and you would need to store the energy somewhere during daytime to cater for nighttime demands. Or you'd need to keep some conventional plants on standby.
Two, if all the power for all the USA were produced in Nevada, you would need to build massive power lines running all across the continent to supply the east coast, for example. Losing a lot in the transfer, so you need even more excess capacity to make up for those losses.
Three, you would need to redeem your investment in that massive solar power plant, so even while sunlight is for free, your solar energy won't be. And you will be competing with existing power providers which already provide 100% of the power required by the US.
Four, while you would create a lot of jobs in the solar panel and power line industry, you would also make a lot of people in other industries lose their job. Coal miners, plant workers etc., and that will run into a lot of resistance from the associated lobby groups.
There are probably a couple more items I have missed. But it's not as easy as "just plaster a couple of square miles with solar panels and we're done".
So, yes, it could be done. But it should be obvious why people are not really eager to do it just that exact way.