Section 2.3 due Sept 10

I don't really understand Theorem 2.8 and what the set of all congruence classes modulo n, with n being a prime number, has to do with ax=1.

The cool thing about this section is that some of the formulas look similar to those that I saw in Linear Algebra, such as Theorem 2.11. The difference is that those dealt with matrices but these equations deal with congruence classes.