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 ?

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SATYANARAYANA R
SATYANARAYANA R on 30 Jul 2020
Commented: John D'Errico on 30 Jul 2020
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 ?

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Answers (1)

KSSV
KSSV on 30 Jul 2020
Calculate the eigenvalues of the product. They will be euqal.
A = rand(2) ;
B = rand(2) ;
AB = eig(A*B)
BA = eig(B*A)

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