Are Multiplicative Inverses in Z_n Equivalent Modulo n?

[kathrynag]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I'm totally confused on this.

 

[kathrynag]

[a]=1 and [a][c]=1, right?