I remember you can define algebras however you like with arbitrary commutativity and associativity rules but in this case you should also apply them and not ass

I remember you can define algebras however you like with arbitrary commutativity and associativity rules but in this case you should also apply them and not assume they work in a certain way. If -1 * -1 = -1, this algebra disallows distributivity rule and the calculation only proves that.