Characteristic Polynomial $AB =$ characteristic polynomial $ BA$?
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
123555
Proving that if $ab=e$ then $ba=e$
116820
If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
76200
Is the rank of $AB$ always equal to the rank of $BA$?
35247
The characteristic and minimal polynomial of a companion matrix
133573
characteristic polynomial of the adjacency matrix of a tree
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
55062
$2\times 2$ matrix $C=AB-BA$
15626
Relations of a~b iff b = ak^2
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
84871
Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
146715
A square matrix has the same minimal polynomial over its base field as it has over an extension field
11654
Where does $xe^x$ solution come from when the characteristic polynomial is square?
66714
Characteristic polynomial of companion matrix
78298
On the nilpotence of the matrix $AB-BA$