It assumes that you already know how modulus works under the hood, which I absolutely did not. The proof for how it's allowed is at the bottom which I would have read first if I'd have known.

If I had a nickle for every time I bookmarked to read later and never did...

It's how you change a number to/from positive/negative.

The basic procedure is to represent the number in binary, invert all the bits, add 1.

It's the technical name of a thing in comp sci, I'm not sure what other answer you want. It specifically contrasts "one's complement".