Question about Proof of Real Number..?

Question

Q: For real numbers a,b show the following by stating the properties used:      i) (-a)b = a(-b) = -ab         ii) (-a)(-b) = ab

Answer 1

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.