solve question 2

1. Let p(x), q(x) be nonzero elements of Z,,[x] where p is a prime. Prove the following: i. deg(p(x)q(x)) = deg(p(x)) + deg(q(x)) ii. The elements in Z,,[x] that have (multiplicative) inverse are exactly the same as the elements with inverse in Z,, 2. Consider the same set up as the previous problem except now we want to consider Z,|x] where n is any positive integer. What could go wrong with the statements made in the previous problem? Provide counter-examples for both statements