1. The problem statement, all variables and given/known data Prove or disprove the following statements concerning 2 x 2 matrices. (a) If A^3 = 5I then A is invertible. (b) If A and B are both invertible then AB - BA is not invertible. (c) If ABC = I then B is invertible. (d) If A^2 - 3A -2I = 0 then (A-1) and (A-2I) are both invertible. (e) If A= EB and E is elementary then B = FA for some elementary F. 2. Relevant equations I am a little confused on the following: What is I? How would I go about proving or disproving any of these, since it depends on the system of vectors in a particular matrix...can I simply do a generic matrix to prove/disprove the statement? Like using constants like a, b, c...etc...? In most cases I know what to do, I just have trouble understanding what the question wants...exactly... 3. The attempt at a solution Thank you!