Show that $\det(A + uv^T) = (1 - v^T(A^{-1}u))\det(A)$
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
106398
If $A$ is invertible show that $\det(A) \neq 0$
30836
Derivative of a determinant whose entries are functions
60900
If $A^2=-I$, Prove that $\det{A}=1$
113518
Determinant of the inverse matrix
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
141792
Slick proof the determinant is an irreducible polynomial
28416
Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
125889
Determinant of rank-one perturbations of (invertible) matrices
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?