Use the properties of addition and multiplication of real numbers given in Prope

Question

Use the properties of addition and multiplication of real numbers given in Properties that
(1) Commutativity. a+b=b+a and ab=ba.
(2) Associativity. (a+b)+c=a+(b+c) and (ab)c=a(bc).
(3) Distributivity. a(b+c)=ab+ac and (a+b)c=ac+bc.
(4) Zero. a+0=a=0+a.
(5) Unity. a*1=a=1*a
(6) Subtraction. The equation a+x=0 has the unique solution x=-a
and so a+x=b<=>x=b+(-a)=b-a.
(7) Division. If a is not equal to zero, then the equation ax=b has the unique solution
x=b/a=b*a^-1.

to deduce that, for all real numbers a and b,
(i) a x 0 = 0 = 0 x a,
(ii) (-a)b= -ab = a(-b)
(iii) (-a)(-b) = ab

Explanation / Answer

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