Thanks in advance for your help (and sorry about the lack of Latex...I didn't know how to type matrices in that format!) The textbook question itself is quite straightforward: Verify that A^2 - A - 6I = 0, given that A is a 2x2 matrix. (I is the identity matrix) It then goes on to provide two examples of A which satisfy that equation. However, I tried to 'play around' with the question. Since we know that AI = A, and I^2 = I, i changed the equation to: A^2 -AI - 6I = 0. This can then be factored into: (A-3I)(A+2I) = 0. However, there are more solutions of 'A' that solve the equation (the ones the textbook provided). My question is...why are there more than 2 solutions? Where have I gone wrong in my reasoning? (I'm self teaching myself Linear Algebra, so I dont' have a teacher to ask about this). Thanks again!