Disprove that AB-BA = I
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Jan6-12, 08:54 AM
What I mean is that I don't know what is det(AB-BA) even if I do know det(AB) and det(BA).
I'm looking at
Sylvester's determinant theorem
which looks related, but I still don't see a solution. Now I need to prove that for no M, det(M+I) = det(M)
, at least when M = AB..
(now that I think about it, there is probably no matrix that can't be written as a product of two others, is there?)
Try taking the trace.