I had asked that how (-)(+) = (-). Brijendra Pal sir answered this to me. 
This was that: 
  
We know that -ab is a unique solution to the equation x + ab =0, therefore it is sufficient yo show that 
ab + (-a)b = 0 
ab + (-a)b = (a + (-a))b
by the Distributive Property of Real Numbers (Axiom 5A) and 
a+(-a) = 0
by Axiom 5A (the existence of Additive Identity). 
Therefore, 
ab + (-a)b = (a +(-a))b = 0b = 0 
and we are done. 
The theorem above give to 2 corollaries. 
Corollary 1 
For any number b, (-1)b = -b 
If we take a = -1, then (-1)b = -(1b) =-b by the existence of multiplicative identity (Axiom 5M). 
(-1)(-1) = 1
I am able to understand what he wrote, but, I am still not getting the Corollary 2 and my teacher also asked, how the Corollary 2 is proved.  Please I want this soon because it is asked by my Maths teacher in school. 
Please experts get into this.