query: When $AB=BA$, form of $A$
positive_passages.docid: 4280
positive_passages.text: A linear operator commuting with all such operators is a scalar multiple of the identity.
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 53113
negative_passages.text: $I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
negative_passages.docid: 13346
negative_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 30923
negative_passages.text: Is the matrix $A^*A$ and $AA^*$ hermitian?
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 84871
negative_passages.text: Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 146795
negative_passages.text: Proof If $AB-I$ Invertible then $BA-I$ invertible.
negative_passages.docid: 147490
negative_passages.text: If matrix $AB=A$, does it mean B must be an identity matrix?
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 6091
negative_passages.text: Similarity of products $AB$ and $BA$ of square matrices
negative_passages.docid: 62770
negative_passages.text: Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
negative_passages.docid: 59397
negative_passages.text: Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
negative_passages.docid: 72092
negative_passages.text: If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
negative_passages.docid: 158406
negative_passages.text: $A,B$ be Hermitian.Is this true that $tr[(AB)^2]\le tr(A^2B^2)$?
negative_passages.docid: 18800
negative_passages.text: If A and B are symmetric is AB=BA true?