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

Question 1184601: Show that R∗=R∖{0} is a group under the operation of multiplication.

Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
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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.

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