Let A and B be square matrices of same order. Prove that characteristic polynomials of AB and BA are same. Do AB and BA have same minimal polynomial ?

Let A and B be square matrices of same order. Prove that characteristic polynomials of AB and BA are same. Do AB and BA have same minimal polynomial ?

[John D'Errico]

This is not a question about MATLAB. Please don't post your homework assignments to Answers.

Answer 1

[KSSV]

Calculate the eigenvalues of the product. They will be euqal.

A = rand(2) ; 
B = rand(2) ; 
AB = eig(A*B) 
BA = eig(B*A)