How to mathematically prove -1 * 1 = 0

ddx

New member
Joined
Dec 8, 2008
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1
Hey all!

I was hoping someone could help me with this proof. Given 1*1 = 1 and -1*-1 = 1 Prove -1*1 =-1.

I thought it would be as simple as stating the multiplicative identity, but my teacher said no.

How might I accomplish it? It's so easy it's hard.

Thanks!
 

chivox

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Joined
Nov 13, 2008
Messages
119
This might be interesting, or it might be trivial. I'm not sure about this one, but have a look at the proof that 1 + 1 = 2, and that might give you some ideas. I'll warn you, though, we're getting into some abstract algebra here, so keep an open mind.

http://mathforum.org/library/drmath/view/51551.html

Just as the proof of 1 + 1 = 2 required a definition for addition, I suspect this one may require a definition of multiplication of integers.
 
B

bertus

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I was hoping someone could help me with this proof. Given 1*1 = 1 and -1*-1 = 1 Prove -1*1 =-1.

1. 1 x 1 = 1 given
2. -1 x -1 = 1 given
3. 1 is the identity under multiplication. From (1) only one number with that property
4. -1 x 1 = 1 x - 1 commutative property
5. 1 x - 1 = 1 definition identity element.
That's my answer but to tell the truth I am not sure what can be assumed here and what can't. Some more background from the text might help.
 

mmm4444bot

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Oct 6, 2005
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bertus said:
5. 1 x - 1 = 1 definition identity element.



Line (5) is not correct.

(1)(-1) = -1

 
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