Let A be an nxn matrix. Is it possible for A^2 + I = 0 in the case where n is odd? What about when n is even? (I is the identity matrix)
Squaring any nxn matrix to achieve (-1) down the main diagonal is impossible, right? Certainly this can't be the answer that they're looking for though. I have a hunch that there's a more eloquent way to say this using determinants, but I don't know for sure... any suggestions?
Thanks in advance!