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.
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...
The Attempt at a Solution