query: Prove that a square matrix with either a left or right inverse is invertible.
positive_passages.docid: 3301
positive_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 148946
negative_passages.text: If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
negative_passages.docid: 8557
negative_passages.text: Invertible Matrices are dense
negative_passages.docid: 146795
negative_passages.text: Proof If $AB-I$ Invertible then $BA-I$ invertible.
negative_passages.docid: 4917
negative_passages.text: Inverse of this $3\times 3$ matrix using the Cayley–Hamilton theorem
negative_passages.docid: 90964
negative_passages.text: Prove: symmetric positive definite matrix
negative_passages.docid: 133449
negative_passages.text: A proof that an orthogonal matrix with a determinant 1 is a rotation matrix
negative_passages.docid: 59133
negative_passages.text: Show that an inverse of a bijective linear map is a linear map.
negative_passages.docid: 53113
negative_passages.text: $I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
negative_passages.docid: 158695
negative_passages.text: Prove that if $AB$ is invertible then $B$ is invertible.
negative_passages.docid: 58561
negative_passages.text: Right and left inverse
negative_passages.docid: 131480
negative_passages.text: Proof that composition of invertible linear transformations is invertible (without determinants)
negative_passages.docid: 92873
negative_passages.text: To prove in a Group Left identity and left inverse implies right identity and right inverse
negative_passages.docid: 115582
negative_passages.text: Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
negative_passages.docid: 97781
negative_passages.text: invertible matrices connected or not
negative_passages.docid: 61538
negative_passages.text: Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
negative_passages.docid: 146487
negative_passages.text: Can a non-square matrix be called "invertible"?