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I need to show that if R is an integral domain and it has unity then the only elements of R which are inverse to itself are 1 and -1 (with respect to multiplication). But I don't know where to start. Can anyone help? Thanks..

user77545
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  • Write it in the form of an equation rather than in the form of an English phrase. –  May 12 '13 at 21:30
  • More generally, any polynomial has number of roots bounded by its degree. – anon May 12 '13 at 21:49

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Here's a hint: $$(x+1)(x-1)=x^2-1.$$

Jonathan
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