I had asked that how: (-)(-)= (+). I saw that in that, (-) (+) = (-)... Prove how(-) (+) = (-)

HI,

We know that –ab is a unique solution to the equation x + ab  = 0, therefore it is sufficient to show that

ab + (-a)b = 0

But

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).

Corollary 2

(-1)(-1) = 1

​Regards

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Is this contain any proof or it is a self-evidence proof by itself? I have heard that there is a proof for this too... What is that?
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If you multiply 1 negative and 1 positive integer together, then you will get a negative integer.
eg-      -2*3= -6
This is rule.
Hope that helps you!!!
Regards...
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Mahima, You are just telling or repeating the same law... But it is definitely not a formal proof. You just repeated the same rule by just taking the example. But can you say how this happened : (-)(+)=(-)? You know when I had asked (-)(-)=(+)..The expert( Brijendra Pal sir) gave me very accurate formal proof using just distributive law or property.. So please be specific...
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This is my last doubt till today..
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(-)(-)=(+) and (-)(+)=(-)
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Krish, the thing you answered is just a law.. O asked to prove how (-)(+)=(-)... Thanking you...
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What are you looking for?