The following is the full syllabus for the course.

In problem 4 b) of the practice final the matrices should have been specified to have real entries.

In problem 4 b) the square of A is wrong one checks that A^3 = -I so A has order 6. Thanks to Shu Peng for pointing out the error.**Solutions for the Math 100A Practice
Final**

The original solution given to problem 1 b) in the practice midterm had an incorrect conclusion. The relation is an equivalence relation it has been fixed in the version below. (Thanks to Ian Langmore for finding the error.)