Proove that $\det(L_B) = \big(\det(B)\big)^n$, $\det(R_B) = \big(\det(B)\big)^n$.
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
69349
If $A$ is positive definite, then $\int_{\mathbb{R}^n}\mathrm{e}^{-\langle Ax,x\rangle}\text{d}x=\left|\det\left({\pi}^{-1}A\right)\right|^{-1/2}$
71442
How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
20921
If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
109312
How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
5183
Divisibility of determinant.
69641
Determinant identity: $\det M \det N = \det M_{ii} \det M_{jj} - \det M_{ij}\det M_{ji}$
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
48660
Proof that determinant rank equals row/column rank
53917
Determinant of matrix exponential?
54740
Proofs of Determinants of Block matrices
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
147207
Is it always true that $\det(A^2+B^2)\geq0$?