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

[rock.freak667]

[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.

 

[rock.freak667]

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

 

[varygoode]

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.