The problem:

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)

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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!