Post #1815093

@hallasurvivor You are probably used to the fact that many matrices can have the same characteristic polynomial, i.e. the fact that a monic polynomial can have more roots than its degree in a non-commutative ring. This cannot happen in commutative rings (the (skew) field property doesn't play a role here). As @trebor remarks, this is related to the fact that evaluation of polynomials is not a homomorphism, a phenomenon that sometimes tricks people into thinking that the Cayley Hamilton theorem should be a triviality which follows from substituting X = A formally in the equation chi(X) = det(X - A).