query: Prove that the determinant of a swap matrix is $-1$
positive_passages.docid: 24873
positive_passages.text: Determinant of elementary permutation matrix
negative_passages.docid: 127085
negative_passages.text: Bound on the difference of two determinants
negative_passages.docid: 113169
negative_passages.text: Number of $\pm 1$ matrices whose determinant is negative or zero
negative_passages.docid: 128723
negative_passages.text: The determinant of adjugate matrix
negative_passages.docid: 155082
negative_passages.text: If $P$ is real orthogonal matrix with $\det P = -1$, prove that $-1$ is an eigenvalue of $P$.
negative_passages.docid: 110825
negative_passages.text: Determinant of circulant matrix
negative_passages.docid: 81770
negative_passages.text: Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant
negative_passages.docid: 79907
negative_passages.text: Determinant of a square matrix in a field
negative_passages.docid: 1865
negative_passages.text: Sub-determinants of an orthogonal matrix
negative_passages.docid: 10083
negative_passages.text: Determinant of matrix times a constant.
negative_passages.docid: 144221
negative_passages.text: Matrix determinant lemma with adjugate matrix
negative_passages.docid: 79031
negative_passages.text: Determinant of the Kronecker Product of Two Matrices
negative_passages.docid: 69980
negative_passages.text: Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
negative_passages.docid: 72326
negative_passages.text: Determinant of block matrix with commuting blocks
negative_passages.docid: 70381
negative_passages.text: Find the determinant of a symmetric matrix
negative_passages.docid: 98646
negative_passages.text: Show determinant of matrix is non-zero
negative_passages.docid: 91028
negative_passages.text: determinant of a matrix with binomial coefficient entries