Count & Describe Automorphisms of Z_3 (Set of Integers Modulo 3)

[erraticimpulse]

Please bear with me as I don't have latex. This is a homework question I have and I don't even know if it makes sense:

How many Z_3 (set of integers modulo 3) vector space automorphisms of Z_3(alpha) are there? Describe them.

I'm not sure if alpha is supposed to be the root of some polynomial or just an element outside of Z_3. I know that Z_3 is isomorphic to GF(3) (the Galois field of order 3). Any help would be much appreciated.

 

[matt grime]

If you don't know what alpha is, then we have no chance of knowing what it is. The only person who can help you here is you: find out from your book, notes, the question sheet, what alpha is.

 

[erraticimpulse]

Okay well, I figured it out. Alpha was defined a few pages earlier as a root of x^2+1 (a polynomial with coeff's in Z_3[x]). Thanks for pointing out what should have been obvious to me.

 

[matt grime]

So Z_3[alpha] is just a 2 dimensional vector space over Z_3, so we're just looking at the invertible 2x2 matrices over Z_3. What answer did you get?