Are Multiplicative Inverses in Z_n Equivalent Modulo n?

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Homework Statement


Show that if and [c] are multiplicative inverses of [a] in [tex]Z_{n}[/tex], then b[tex]\equiv[/tex]c mod n.


Homework Equations





The Attempt at a Solution


I'm totally confused on this.
 
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[a]=1 and [a][c]=1, right?