- #1
Mr Davis 97
- 1,462
- 44
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.
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?
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?