SOLUTION: Show that R∗=R∖{0} is a group under the operation of multiplication.

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Question 1184601: Show that R∗=R∖{0} is a group under the operation of multiplication.
Answer by ikleyn(52748) About Me  (Show Source):
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Show that R* = R∖{0} is a group under the operation of multiplication.
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You should check or prove that

        - (1)   the product of any two elements of  R*  does belong to  R*;

        - (2)   the unit element does belong to  R*;

        - (3)   the inverse element to any element of  R*  does belong to  R*.


All three statements/steps are  OBVIOUS.

I want to say that their proofs are obvious for every statement.