Hi, I need some help with this question.
Let be a field and .
a. The numbers of bases of for is equal to the order of
b. Prove the order of is .
c. Prove the order of is .
If is a basis of then there is an invertible matrix with these vectors as columns.
Note that can be any non-zero vector, then can be any vector in that is not on the line spanned by , and same for to . So there are choices for , choices for , choices for , etc.
So the order of is
So this gives me the answer to part b, but how do I work out part a and c?
Thanks for any help you provide.