How to find the inverse of an element in a group?
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There is no "division operation" in a group, it only signifies a/b=ab−1 So you are right to say that 1/3 is the inverse of 3, but a better notation would be 3−1. Now, to see that 3 and 7 are inverses in the group of units mod 10, we see that 3⋅7=21≡1(mod10) and 1 is the identity. We xan do the same to find the inverse of 9.
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