Let R = {0,2,4,6,8} under addition and multiplication in Mod 10. Prove that R is a field.

My proof so far:

I understand that I need to prove there exist a unity in R, and for all nonzero elements in R, there exist their inverses.

Now, I found that 6 is the unity because for all elements a in R, 6a = a in Mod 10.

However, I have a bit of difficulty prove all elements are units.

Little help?