query: If $A,B\in \mathbb R^{n\times n}$ s.t. $AB=I$ then $BA=I$.
positive_passages.docid: 3301
positive_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 81868
negative_passages.text: How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 105921
negative_passages.text: Why do we have $ab=ba$?
negative_passages.docid: 18693
negative_passages.text: If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
negative_passages.docid: 133482
negative_passages.text: $AB-BA$ is a nilpotent matrix if it commutes with $A$
negative_passages.docid: 20878
negative_passages.text: If $(a,b)=1$ then prove $(a+b, ab)=1$.
negative_passages.docid: 136448
negative_passages.text: $ABAB=0_{n\times n}$, then must $BABA$ be $0_{n\times n}$?
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: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 77902
negative_passages.text: If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
negative_passages.docid: 71012
negative_passages.text: If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
negative_passages.docid: 30583
negative_passages.text: If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 141173
negative_passages.text: Are there matrices such that $AB=I$ and $BA \neq I$
negative_passages.docid: 120094
negative_passages.text: Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
negative_passages.docid: 99631
negative_passages.text: Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$