query: $AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
positive_passages.docid: 13346
positive_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 99585
negative_passages.text: Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
negative_passages.docid: 17032
negative_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 41514
negative_passages.text: Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 115782
negative_passages.text: Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
negative_passages.docid: 73677
negative_passages.text: If the matrix $A^3 = 0$, is $A$ singular?
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 39788
negative_passages.text: $a+1,a-1$ invertible for nilpotent element
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 144266
negative_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$
negative_passages.docid: 22563
negative_passages.text: Units and Nilpotents
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 106442
negative_passages.text: Show that AB is singular if A is singular
negative_passages.docid: 60707
negative_passages.text: Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
negative_passages.docid: 156443
negative_passages.text: if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$