Prove for all n > 1 that Z/nZ is not a group under multiplication of residue classes.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 20E: Consider the group U9 of all units in 9. Given that U9 is a cyclic group under multiplication, find...
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Please explain the following question, I know the answer mentions that 0 has no multiplicative inverse but I cant follow it, why are we looking at 0 when the question states n has to be greater than 1? Im very confused so please if able give a full explanation. Thank you in advance.

Prove for all n > 1 that Z/nZ is not a group under multiplication of residue classes.
Transcribed Image Text:Prove for all n > 1 that Z/nZ is not a group under multiplication of residue classes.
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May sound like an obvious question but how does the set contain 0 when n is greater than 1?

 

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