Are matrices $AB~BA$ similar? (where $A$ and $B$ are not necessary singular)
6091
Similarity of products $AB$ and $BA$ of square matrices
57515
Similar matrices and field extensions
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
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.
94037
Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
32767
Similar Matrices and Linear Transformations
93531
Do commuting matrices share the same eigenvectors?
31116
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
106442
Show that AB is singular if A is singular
27767
Are two matrices similar iff they have the same Jordan Canonical form?
3301
If $AB = I$ then $BA = I$
116820
If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
104653
$A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
147903
Similar matrices-Identity
3330
Square matrices, ABA = A?