Homework solutions not on the TA's course page:
Errata for the text by Childs.
Complex demos:
For finding the inverse, people are having trouble interpreting the suggestion. Just take the equation α8 = α4 + α3 + ... + 1, multiply through by α-1, to get α7 = α3 + α2 + ... + α-1, and then solve for α-1, remembering that in the two-element field -1 = 1 so minus an expression is the same as plus the expression. (Of course, α is just one element of the field and this method of inverting applies only to α itself.)