0 =[absorption] 0 * 0 =[def 0] (1-1)(1-1) =[distributivity] 1*1 + 1*-1 + -1*1 + -1*-1 =[def 1] 1 -1 -1 + -1*-1 =[eval] -1 + -1*-1 =[def 0] -1 + -(-1) =[def 0]  -1 + 1

therefore -1*-1 =[by left cancellation] 1