If $A=AB-BA$, is $A$ nilpotent?
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
74318
Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
123555
Proving that if $ab=e$ then $ba=e$
8638
If I know $AB$, how can I calculate $BA$?
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
22563
Units and Nilpotents
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
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?
72507
Does $ab=1$ imply $ba=1$ in a ring?
37867
If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
55062
$2\times 2$ matrix $C=AB-BA$
28460
Show matrix is nilpotent