How can we prove that -1*-1=1?

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SUMMARY

The proof that -1*-1=1 can be established through algebraic manipulation and understanding of zero. Starting from the equation 0 = (1 + (-1)), one can derive that 0*0=0 leads to the conclusion that (-1*-1)-1=0. Thus, it follows that -1*-1 must equal 1. This proof utilizes basic properties of numbers and algebraic identities to demonstrate the validity of the equation.

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[SOLVED] -1*-1=1 ? how to prove

Homework Statement


Well as the subject states..how does one prove that -1*-1=1?
I think you have to use proof by contradiction but I don't know what to do after assuming that it is not true.
 
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Ok I think I got it...I was told that I should start by knowing that 0*0=0 and that 1-1=0
such that 0*0=0 => (-1+1)*(-1+1)=(-1*-1)-1-1+1=0
(-1*-1)-1=0
and so -1*-1=1
 
Well, think about what you know about (-1).

Then, think about what you know about (0).

More specifically, note:

0 = (1 + (-1)) and 0 = ((-1)+1)

AND

0 = 0*0.

You should be able to get the algebraic proof from there.

EDIT: Dang, you got it already. Good job, but don't double post, just edit your original post.
 

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