query: Let $A, B$ be square matrices. If $A B = A + B$, then $A B = B A$.
positive_passages.docid: 6096
positive_passages.text: If $A+B=AB$ then $AB=BA$
negative_passages.docid: 60006
negative_passages.text: Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
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: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 141173
negative_passages.text: Are there matrices such that $AB=I$ and $BA \neq I$
negative_passages.docid: 127296
negative_passages.text: prove that a|b and b|a iff a=+-b
negative_passages.docid: 63931
negative_passages.text: When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
negative_passages.docid: 153670
negative_passages.text: Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
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: 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: 82410
negative_passages.text: Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
negative_passages.docid: 78755
negative_passages.text: If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?
negative_passages.docid: 13026
negative_passages.text: Prove that if AB=I_m, then rk(A)=rk(B).
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: 11895
negative_passages.text: If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
negative_passages.docid: 115296
negative_passages.text: Under what conditions does a matrix $A$ have a square root?