Question 935113: Is (R-{0},*) a group, how to prove it...
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Consider, (R*,*) where R* = R - {0} IS a group.
multiplication in R is associative, so remains associative on any subset of R.
the product of two non-zero real numbers is again a non-zero real number, R* is closed under multiplication.
1 functions as a multiplicative identity:
for any NON-ZERO real number a, a*1 = 1*a = a.
any non-zero real number a has a (unique) inverse, 1/a, with
a*(1/a) = (1/a)*a = 1.
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