query: $A \in \mathbb{Z} ^{n \times n}$. Show that $\det(A) = \pm 1$.
positive_passages.docid: 17584
positive_passages.text: Integer matrices with integer inverses
negative_passages.docid: 106584
negative_passages.text: If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
negative_passages.docid: 62382
negative_passages.text: I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
negative_passages.docid: 133756
negative_passages.text: Geometric interpretation of $\det(A^T) = \det(A)$
negative_passages.docid: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
negative_passages.docid: 117688
negative_passages.text: Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
negative_passages.docid: 152637
negative_passages.text: Determinant of a specific circulant matrix, $A_n$
negative_passages.docid: 127978
negative_passages.text: Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic.
negative_passages.docid: 67784
negative_passages.text: If $A + A^t = 2I$ then $\det(A) \geq 1$
negative_passages.docid: 60777
negative_passages.text: Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
negative_passages.docid: 141909
negative_passages.text: Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
negative_passages.docid: 131212
negative_passages.text: Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
negative_passages.docid: 78218
negative_passages.text: $A \in M_3(\mathbb Z)$ be such that $\det(A)=1$ ; then what is the maximum possible number of entries of $A$ that are even ?
negative_passages.docid: 49578
negative_passages.text: Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 96152
negative_passages.text: Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
negative_passages.docid: 63119
negative_passages.text: Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.