Let A and B be nxn matrices over an arbitary field such that AB = -BA. Prove that if n is odd then A or B is not invertible.(adsbygoogle = window.adsbygoogle || []).push({});

This is rather easy when we use determinants. However, I am curious, how hard would it be to prove this without the use of determinants? What would be involved in such a proof, and how much more work would it be when compared to just using determinants?

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# I Proving a result about invertibility without determinants

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