RE: [Math4u] can this be proved

If I recall correctly, yes.

 

Start with:

 

1 + (-1) = 0 (because -1 is the additive inverse of 1)

 

Multiply the above by -1:

 

(-1)*(1 + (-1)) = 0

(-1)*1 + (-1)*(-1) = 0 (because multiplication is distributive)

-1 + (-1)*(-1) = 0 (because 1 is the identity under multiplication)

 

Add -1 to both sides:

-1 + (-1)*(-1) + 1 = 0 + 1

-1 + (-1)*(-1) + 1 = 1 (because 0 is the identity under addition)

(1 + -1) + (-1)*(-1) = 1 (because addition is commutative)

0 + (-1)*(-1) = 1 (because -1 is the inverse of 1)

(-1)*(-1) = 1 (because 0 is the identity under addition)

 

... hopefully, I haven't missed out any steps!

 

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From: Math4u@yahoogroups.com [mailto:Math4u@yahoogroups.com] On Behalf Of Julien Santini
Sent: 12 October 2007 09:04
To: Math4u@yahoogroups.com
Subject: Re: [Math4u] can this be proved

This is by definition of the operation multiplication
over the ring of the integers.

http://www.mymathforum.com
Julien

--- Sarthak Chandra <sarthak_loves_math@yahoo.co.in>
wrote:

> prove
> -1 * -1 = +1
>
>
> ---------------------------------
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