query: If $A$ and $B$ are nxn matrices such that $BA =I$ , does it follow that $AB=BA$? If so,explain.
positive_passages.docid: 3301
positive_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 15416
negative_passages.text: A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
negative_passages.docid: 6091
negative_passages.text: Similarity of products $AB$ and $BA$ of square matrices
negative_passages.docid: 13346
negative_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?
negative_passages.docid: 151443
negative_passages.text: Find two $2 \times 2$ matrices $A$ and $B$ with the same rank, determinant,...but they are not similar.
negative_passages.docid: 129007
negative_passages.text: Relation between AB and BA
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 18800
negative_passages.text: If A and B are symmetric is AB=BA true?
negative_passages.docid: 48658
negative_passages.text: Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
negative_passages.docid: 58021
negative_passages.text: Finding matrix $B$ is not zero matrix where $AB= 0$
negative_passages.docid: 120867
negative_passages.text: How prove this two symmetric matrices $AB=0$
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 62770
negative_passages.text: Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 139934
negative_passages.text: In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
negative_passages.docid: 6096
negative_passages.text: If $A+B=AB$ then $AB=BA$