query: If $A$ is an $m \times n$ matrix and $B$ is an $n \times m$ matrix and $n<m$, then the product $AB$ is not invertible.
positive_passages.docid: 25682
positive_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: 103142
negative_passages.text: Question on equivalence of inner product
negative_passages.docid: 120094
negative_passages.text: Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
negative_passages.docid: 141105
negative_passages.text: Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
negative_passages.docid: 112701
negative_passages.text: Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
negative_passages.docid: 6398
negative_passages.text: Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?
negative_passages.docid: 30049
negative_passages.text: If $T^m$ is diagonalizable for a $m\in\mathbb N$, then $T$ is diagonalizable.
negative_passages.docid: 119301
negative_passages.text: Is the following matrix invertible?
negative_passages.docid: 33355
negative_passages.text: Proving that matrix in equation is invertible
negative_passages.docid: 10911
negative_passages.text: $A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
negative_passages.docid: 90402
negative_passages.text: $AB$ is not invertible
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 70723
negative_passages.text: Why are nonsquare matrices not invertible?
negative_passages.docid: 140103
negative_passages.text: If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
negative_passages.docid: 4517
negative_passages.text: Showing a $2\times2$ matrix is invertible
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: 61103
negative_passages.text: Prove that $\mathbb{|Q| = |Q\times Q|}$