text: please prove: (-a)b = -(ab); (-1)b = -b. please use axioms only? please, also prove this: (-a)(-b) = ab. again, please use axioms... thanx a lot... using b•0=0 (already proved this for you) b•0=b(1-1)=b+(-1)•b=0. (distributive property a(b+c)=ab+ac) therefore -b+b+(-1)b=(-1)b=0+-b=-b (adding inverse, equivalent to cancellation property)  now using (-1)x=-x for all x: (-a)b=((-1)a)b=(-1)(ab)=-ab (associativity (ab)c=a(bc))