Let A and B be square matrices of same order. Are the characteristic polynomials of AB and BA same? A and B may be invertible or not.
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
131611
$A^TA$ is always a symmetric matrix?
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
106493
Coefficients of characteristic polynomial of a matrix
146715
A square matrix has the same minimal polynomial over its base field as it has over an extension field
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
66709
Are the matrix products $AB$ and $BA$ similar?
6096
If $A+B=AB$ then $AB=BA$
27767
Are two matrices similar iff they have the same Jordan Canonical form?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
73027
Questions on symmetric matrices
33891
If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots?
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
106322
Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.
66714
Characteristic polynomial of companion matrix