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?