query: $A,B$ both are singular matrix and also rank $AB$ = rank $BA$. Then is the following true?
positive_passages.docid: 31606
positive_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 49330
negative_passages.text: If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
negative_passages.docid: 78755
negative_passages.text: If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 65628
negative_passages.text: what happens to rank of matrices when singular matrix multiply by non-singular matrix??
negative_passages.docid: 106442
negative_passages.text: Show that AB is singular if A is singular
negative_passages.docid: 55820
negative_passages.text: If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
negative_passages.docid: 25682
negative_passages.text: If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
negative_passages.docid: 74460
negative_passages.text: Matrices A+B=AB implies A commutes with B
negative_passages.docid: 95227
negative_passages.text: Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
negative_passages.docid: 2798
negative_passages.text: A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
negative_passages.docid: 58021
negative_passages.text: Finding matrix $B$ is not zero matrix where $AB= 0$
negative_passages.docid: 9574
negative_passages.text: How to show that $\det(AB) =\det(A) \det(B)$?
negative_passages.docid: 48660
negative_passages.text: Proof that determinant rank equals row/column rank
negative_passages.docid: 29454
negative_passages.text: A and B are real, symmetric and positive semi-definite matrices of the same order; is AB diagonalizable?
negative_passages.docid: 145876
negative_passages.text: $AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.