Is the following statement true? AB and BA have the same minimal polynomial

No. A = [[0,1],[0,0]], B = [[0,0],[0,1]] AB = A has minimal polynomial x², BA = 0 has x. The characteristic polynomials do agree.

Counterexample

Is this true?

AB and BA have the same minimal polynomial

No — it is false.

The counterexample

A = [[0,1],[0,0]], B = [[0,0],[0,1]]

Why it fails

AB = A has minimal polynomial $x^{2}$ , BA = 0 has x. The characteristic polynomials do agree.

Keep practicing

Execution slip

The idea was right. The computation was not.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.