Show that $\lvert \mathbb Z^n / N\rvert = \lvert \det (A) \rvert$.
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
55232
Show that $g\circ f\equiv 0$ implies $\det Df\equiv 0$, where $g(x_1,...,x_n)=x_1^5+...+x_n^5$
116376
Prove the determinant is the product of its diagonal entries
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
106398
If $A$ is invertible show that $\det(A) \neq 0$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
14646
Prove $\det(kA)=k^n\det A$
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?