galois theory - Multiplicative Inverse in $GF(2^8)$ using Extended Euclidiean Algorithm.

We know that the AES S-box is generated by determining the multiplicative inverse of a given number in GF$(2^8)$. Considering this information, we have to explain:

what is $\{07\}^{-1}$ in GF$(2^8)$? This problem must be solved with Extended Euclidean algorithm.

Could someone please explain how to do this with a step by step example?