Hi all, I am going through a Algebra textbook and I need a bit of help with this question, so thank you in advance for any help.

Question: Prove that the set of symbols forms a field with nine elements, if the laws of composition are made to mimic addition and multiplication of complex numbers. Will the same method work for ? For ? Explain.

So I can see that the nine elements are: but I am confused as to where to go from here.

June