query: Complex matrixes $A$, $B$ such that $AB - BA = B$. Prove that $0$ is the only eigenvalue of $B$.
positive_passages.docid: 145876
positive_passages.text: $AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
negative_passages.docid: 10828
negative_passages.text: If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
negative_passages.docid: 76200
negative_passages.text: Is the rank of $AB$ always equal to the rank of $BA$?
negative_passages.docid: 16439
negative_passages.text: What are the eigenvalues of matrix that have all elements equal 1?
negative_passages.docid: 104293
negative_passages.text: How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
negative_passages.docid: 110502
negative_passages.text: $AB=BA$ with same eigenvector matrix
negative_passages.docid: 74460
negative_passages.text: Matrices A+B=AB implies A commutes with B
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 6096
negative_passages.text: If $A+B=AB$ then $AB=BA$
negative_passages.docid: 153392
negative_passages.text: Let $A$ be a $n\times n$ matrix such that $a_{ij}=ij$,find the eigenvalues of the matrix $A$.
negative_passages.docid: 145980
negative_passages.text: For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
negative_passages.docid: 119387
negative_passages.text: If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 98323
negative_passages.text: If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
negative_passages.docid: 128760
negative_passages.text: If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
negative_passages.docid: 84422
negative_passages.text: $AB=BA$, $AC=CA$ we need to show $BC=CB$
negative_passages.docid: 12927
negative_passages.text: $A^2+B^2=AB$ and $BA-AB$ is non-singular