query: Why is the inverse of a matrix with entries $\frac {1}{i+j}$ an integer matrix?
positive_passages.docid: 25159
positive_passages.text: Why does the inverse of the Hilbert matrix have integer entries?
negative_passages.docid: 116136
negative_passages.text: Proof that the inverse of a square matrix is unique
negative_passages.docid: 143629
negative_passages.text: Looking for insightful explanation as to why right inverse equals left inverse for square invertible  matrices
negative_passages.docid: 36064
negative_passages.text: How many $3 \times 3$ integer matrices are orthogonal?
negative_passages.docid: 146534
negative_passages.text: Find out trace of a given matrix $A$ with entries from $\mathbb{Z}_{227}$
negative_passages.docid: 125021
negative_passages.text: Inverse of an invertible upper triangular matrix of order 3
negative_passages.docid: 20611
negative_passages.text: Inverse of a factorial
negative_passages.docid: 121767
negative_passages.text: Why $\det(A^{-1}) = 1/\det(A)$?
negative_passages.docid: 74341
negative_passages.text: Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
negative_passages.docid: 58491
negative_passages.text: Proving the inverse of a matrix as a polynomial of matrices
negative_passages.docid: 50010
negative_passages.text: Is this how eigenvalues of some matrix $A$ are related to the inverse of $A$?
negative_passages.docid: 99815
negative_passages.text: Dividing versus multiplying by inverse in modular arithmetic
negative_passages.docid: 84279
negative_passages.text: The average determinant of all integer matrices with coefficients $0,1,2$
negative_passages.docid: 119301
negative_passages.text: Is the following matrix invertible?
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: 35015
negative_passages.text: Why must the determinant of a matrix with with integer entries be an integer?
negative_passages.docid: 4509
negative_passages.text: Proof that an involutory matrix has eigenvalues 1,-1