I'm given the field for which I need to calculate the inverse of each element.
I assume the way to do this is similar to the Extended Euclidean Algorithm and this is what I have for computing the inverse of . I'm a little bit skeptical with my reasoning however and this is partially due to my lack of familiarity of working with polynomials over .
1) First use the Division algorithm to obtain
From the above, this gives us .
On the other hand, as we are working over , it follows that we must have since . Hence the inverse of is just .
Is this correct?