what happens if you short the output on an inverting amplifier to its
inverting input?
You get a zero-gain inverter. I saw one of these in use once, and
my engineer was baffled by it. "What the heck is a zero-gain inverter
for?" and you could almost see the question marks around his head
like in the cartoons.
It provides a virtual ground. I believe that the reason for doing
it that way has something to do with temperature compensation or
input offset current of the downstream devices.
Or, if you lift the non-inverting input, it's a voltage follower.
Cheers!
Rich