I just finished a final in a linear algebra course and was unsure about one of the questions. The question was: If A^2 - A + I = 0 , show that A is invertible. My approach was that det(A^2 + I) = det(A) det(A^2 + I) will never be zero, so det(A) is non-zero and therefore A is invertible. Is this the right way of doing this problem? Thanks!