let F4 = (0,1,a,b) be a field containing 4 elements.

Assume 1+ 1 = 0

Prove that b = a^-1 = a^2 = a + 1

What i did:

if b = a^-1

then b.a = (a^-1).(a)

so ab = 1

How can i prove the whole in equality?

Where do i go from here?

Any advice will be helpfull.

Thanks