It seems you wrote the field with 9 elements.

Now , I don't know what is or whatever it was you wrote, but perhaps the intention was to

calculate the powers of and, thus, show that this is an

element of order 8, thus showing that is a cyclic group...

But then I don't understand why did you divide ...??

Explain better your symbols and what exactly have you done.

Anyway, it's easy to check that and thus indeed has order 8 in the multiplicative group of the field.

Tonio