$C$ is a square matrix and $\operatorname{tr}(C)=0$ are there matrices $A$ and $B$ in which $C=AB-BA$?
140290
Solving $AB - BA = C$
34759
Name of a special matrix
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
151443
Find two $2 \times 2$ matrices $A$ and $B$ with the same rank, determinant,...but they are not similar.
105921
Why do we have $ab=ba$?
41514
Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
58021
Finding matrix $B$ is not zero matrix where $AB= 0$
152831
When does a complex matrix have a square root?
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
44596
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
8920
There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
120867
How prove this two symmetric matrices $AB=0$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
12213
Similarity of real matrices over $\mathbb{C}$