query: Are there matrices such that $AB=I$ and $BA \neq I$
positive_passages.docid: 3301
positive_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 78755
negative_passages.text: If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?
negative_passages.docid: 105921
negative_passages.text: Why do we have $ab=ba$?
negative_passages.docid: 133482
negative_passages.text: $AB-BA$ is a nilpotent matrix if it commutes with $A$
negative_passages.docid: 52882
negative_passages.text: find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
negative_passages.docid: 31606
negative_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 128990
negative_passages.text: Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
negative_passages.docid: 123555
negative_passages.text: Proving that if $ab=e$ then $ba=e$
negative_passages.docid: 122622
negative_passages.text: Does there exist a matrix $P$ such that $P^n=M$ for a special matrix $M$?
negative_passages.docid: 39353
negative_passages.text: Matrices that can only be permutation matrices
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 8920
negative_passages.text: There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
negative_passages.docid: 85581
negative_passages.text: Matrices commute if and only if they share a common basis of eigenvectors?
negative_passages.docid: 106322
negative_passages.text: Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.
negative_passages.docid: 35080
negative_passages.text: If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
negative_passages.docid: 43570
negative_passages.text: Finding two non-zero matrices where $AX = BA$
negative_passages.docid: 16250
negative_passages.text: If $B_1,B_2$ and $B_2,B_3$ are MUBs, can we conclude that either $B_1,B_3$ are MUBs, or they have equivalent Hadamard matrices?