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!
I follow you until you get to . With either a 3x3 or 4x4 matrix you get a determinant of 1 after squaring them. In both cases the determinants alone become for the original equation. Thus it fails in either case-- odd or even. Can you explain what I'm missing in regards to the part?
Thanks for the help by the way!