Exercise 4. Group theory [10 points] Option 1: basic problem Show that the set of 3 2 matrices with real entries is a group under matrix addition. Option 2: advanced problem Show that every group G = {e, a, b} with three elements is commutative. Hint: You may use that (for any group) each group element has exactly one inverse, and each element commutes with its inverse. (If you would like, you can also prove these statements!)