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IMC 2000 Day 2 Problem Solutions by Muhammad Al Kahfi is a document available to read on EtoBox.

The solution provides three key points: 1) It proves that the characteristic polynomials of q(eAB) and q(eBA) are the same for any polynomial q and matrices A and B. 2) If p(eAB) is nilpotent, then choosing q = pk shows that q(eAB) = 0. 3) Since the characteristic polynomials are the same, q(eBA) = 0 as well, so p(eBA) must also be nilpotent. Therefore, the statement is proven to be true - a polynomial p of eAB is nilpotent if and only if p of eBA is nilpotent.

Author

Muhammad Al Kahfi

Language

EN