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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..

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  • $\begingroup$ Write it in the form of an equation rather than in the form of an English phrase. $\endgroup$ – user14972 May 12 '13 at 21:30
  • $\begingroup$ More generally, any polynomial has number of roots bounded by its degree. $\endgroup$ – anon May 12 '13 at 21:49
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Here's a hint: $$(x+1)(x-1)=x^2-1.$$

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