Let c be a real number, then the associative rule says that (a*b)*c=a*(b*c); the commutative rule says that a*b=b*a, a*c=c*a and b*c=c*b. a*c=a*-1=c*a=-1*a=-a and b*c=c*b=-1*b=-b, when c=-1.
(-a)(b)=(ca)b=(ac)b=a(cb)=a(-b).
Let x=c*c=c^2=(-1)^2=1. (ca)(cb)=(ac)(cb)=a(c*c)b by the associative rule=a(x)b=(xa)b=x(ab)=1(ab)=ab.