Solved: False - Product of Two Nonunits in Z_n Cannot be Unit

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[SOLVED] ring theory problem

Homework Statement


True or false. The product of two nonunits in Z_n may be a unit.


Homework Equations





The Attempt at a Solution


If a and b are two non units in Z_n, and ab <= n, then the result is clear, since ab would not be relatively prime to n. But what about if ab > n ?
Obviously the units form a group under multiplication, but I don't see how that helps.
 
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i don't see how it matters we are in Z_n,

if a and b are not units in a commutative ring R, then ab is not a unit, if it was then ..some stuff..
 
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If ab were a unit, then we would have abc=1, for some c. This implies that a(bc)=1 which implies that a is a unit.

Is that it?
 
of course yea! (just also notice by commutativity (bc)a = 1 too of course, but that's obvious)