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Why -1×-1=+1? Why the product of two negative numbers is a positive number?

Why -1×-1=+1? Why the product of two negative numbers is a positive number?

Grade:12

1 Answers

Arun
25758 Points
4 years ago
Dear student...
 
I am giving its prrof by another approach-
let's take ,
x=ab+(-a)b+(-a)(-b)
  • now lets consider factor of (-a),
(-a)b+(-a)(-b)
so x=ab+(-a)(b+(-b)
But, (b+(-b))=0.
so, x=ab ....result1
  • lets consider factor of b,
ab+(-a)b
so x=b(a+(-a))+(-a)(-b).
buts 
(a+(-a))=0.
x=(-a)(-b) ....result2
From result1 and result2 x=ab=(-a)(-b)

The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.

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