Proof: (-1)(-1) = 1

(-1)(-1) must equal 1 or -1

Let us assume that (-1)(-1) = -1

(-1)(0) = (-1)(1-1)

(-1)(0) = (-1)(1) + (-1)(-1)

(-1)(0) = -1 + (-1) { from our original assumption of (-1)(-1) = -1 }

(-1)(0) = -1 - 1

(-1)(0) = -2

And since we know any number times zero is zero

0 = -2 is false and so is our assumption that (-1)(-1) = -1

Therefore:

(-1)(-1) = 1

PROOF BY CONTRADICTION