[Math4u] Re: can this be proved

Greetings:

-1 + 1 = 0  [definition of additive inverse]

-1 * 0 = 0  [r*0=0*r for all r in R]

-1 * (-1 + 1) = 0  [substitution, line #1 into #2]

(-1*-1) + (-1*1) = 0  [multiplication is distributive over addition in (R, +, *)]

(-1*-1) + (-1) = 0  [definition, multiplicative identity] 

By the definition of 'additive inverse', r'+r = 0 iff r' is the (+)inverse of r; r in R.  Hence, (-1*-1) is the (+)inverse of -1.  But 1 is the (+)inverse of -1.  Because the additive inverse of r is unique for all r in R, it therefore follows that -1*-1 = 1 and the proof is complete.   

Regards,

Rich B.        

 

--- In Math4u@yahoogroups.com, Sarthak Chandra <sarthak_loves_math@...> wrote:
>
> prove
> -1 * -1 = +1
>
>
> ---------------------------------
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