query: if B is n square matrix anad invertible then $\text{rank}(AB)=\text{rank}(A)$
positive_passages.docid: 26570
positive_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 75215
negative_passages.text: Properties of invertible matrices
negative_passages.docid: 122580
negative_passages.text: If N is elementary nilpotent matrix, show that N Transpose is similar to N
negative_passages.docid: 123275
negative_passages.text: Prove $[A,B^n] = nB^{n-1}[A,B]$
negative_passages.docid: 153506
negative_passages.text: Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
negative_passages.docid: 125889
negative_passages.text: Determinant of rank-one perturbations of (invertible) matrices
negative_passages.docid: 21758
negative_passages.text: Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
negative_passages.docid: 121157
negative_passages.text: Proof verification: column rank = row rank
negative_passages.docid: 129564
negative_passages.text: Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
negative_passages.docid: 76200
negative_passages.text: Is the rank of $AB$ always equal to the rank of $BA$?
negative_passages.docid: 8787
negative_passages.text: In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
negative_passages.docid: 131701
negative_passages.text: Why is $A^TA$ invertible if $A$ has independent columns?
negative_passages.docid: 27248
negative_passages.text: If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
negative_passages.docid: 146847
negative_passages.text: Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
negative_passages.docid: 153823
negative_passages.text: $|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
negative_passages.docid: 46128
negative_passages.text: Representation of Matrix with Rank 1
negative_passages.docid: 6905
negative_passages.text: Rank of product of a matrix and its transpose