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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.

$ForCorollary2:\phantom{\rule{0ex}{0ex}}Ifwetakea=-1andb=-1\phantom{\rule{0ex}{0ex}}ab=\left(-1\right)\times \left(-1\right)=-(-1)=1$

Regards

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