Using any multiplication and addition axioms that you know, prove this theorem.

If each of x and y is a number, then

Part one: (-x)*y = -(x*y) = x*(-y) and

Part two: (-x)*(-y) = x*y.

Part three: Also, if x is a number, then (-1)*x = -x. (-1)*(-1) = 1.

I think it would obviously be easier to do each part separately but I don't know where to start. I'm sure it would be useful to use the definition of minus x in there somewhere, too.