query: $A^2+B^2=AB$ and $BA-AB$ is non-singular
positive_passages.docid: 27984
positive_passages.text: Square matrices satisfying certain relations must have dimension divisible by $3$
negative_passages.docid: 13914
negative_passages.text: If $a^2+b^2=c^2$ then $a$ or $b$ is even.
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: 158724
negative_passages.text: Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 78298
negative_passages.text: On the nilpotence of the matrix $AB-BA$
negative_passages.docid: 73697
negative_passages.text: Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 106986
negative_passages.text: Eigenvalues of $AB$ and $BA$
negative_passages.docid: 157863
negative_passages.text: A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
negative_passages.docid: 43570
negative_passages.text: Finding two non-zero matrices where $AX = BA$
negative_passages.docid: 115460
negative_passages.text: Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
negative_passages.docid: 24809
negative_passages.text: For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 141173
negative_passages.text: Are there matrices such that $AB=I$ and $BA \neq I$
negative_passages.docid: 84422
negative_passages.text: $AB=BA$, $AC=CA$ we need to show $BC=CB$
negative_passages.docid: 18800
negative_passages.text: If A and B are symmetric is AB=BA true?