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**1. Homework Statement**

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. Homework 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!