query: If A and B are square matrices of same order such that AB=A+B then prove that AB=BA
positive_passages.docid: 6096
positive_passages.text: If $A+B=AB$ then $AB=BA$
negative_passages.docid: 89329
negative_passages.text: If a and b are relatively prime and ab is a square, then a and b are squares.
negative_passages.docid: 8356
negative_passages.text: Any $n \times n$ matrix $A$ can be written as $A = B + C$ with $B$ is symmetric and $C$ skew-symmetric.
negative_passages.docid: 110381
negative_passages.text: Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
negative_passages.docid: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 43570
negative_passages.text: Finding two non-zero matrices where $AX = BA$
negative_passages.docid: 158724
negative_passages.text: Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
negative_passages.docid: 4141
negative_passages.text: Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
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: 158845
negative_passages.text: Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
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: 84422
negative_passages.text: $AB=BA$, $AC=CA$ we need to show $BC=CB$
negative_passages.docid: 94037
negative_passages.text: Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
negative_passages.docid: 84626
negative_passages.text: Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
negative_passages.docid: 25488
negative_passages.text: Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
negative_passages.docid: 70827
negative_passages.text: Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$