Question

The order of $\left[7\right]$ in $(z_9,{+}_9)$ is:

• A. $9$
• B. $6$
• C. $3$
• D. $1$

Answer 1

Answer: (A)

$9$

We have to find the order of $\left[7\right]$ in $(Z_9,{+}_9)$.

In $(Z_9,{+}_9)$ the identity element is $\left[0\right]$. That is, $e=\left[0\right]$.

We know that, $\left[7\right]+\left[7\right]+\left[7\right]+...+\left[7\right]\left(9times\right)=63=\left[0\right]\left(mod9\right)$

Thus order of $\left[7\right]$ is $9$.