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The order of $[7]$ in $(Z_{9},+_{9})$ is

\[\begin{array}{1 1}(1)9&(2)6\\(3)3&(4)1\end{array}\]

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$Z_9= \{[0],[1],[2],[3],[4],[5],[6],[7],[8]\}$
The identity element in $Z_9$ is $[0]$
The least value of n such that 7n is a multiple of 9.
ie $n=9$
Hence 1 is the correct answer.
answered May 22, 2014 by meena.p
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