Proving that $\det (M) = \det (A) \det(D-CA^{-1}B)$
63119
Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
101313
Minimal polynomial, determinants and invertibility
54740
Proofs of Determinants of Block matrices
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
79031
Determinant of the Kronecker Product of Two Matrices
52750
Prove that $f^\ast\omega=\det f \cdot \omega$
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$
135252
If $M$ is positive definite, then $\operatorname{det}{(M)}\leq \prod_i m_{ii}$
106619
Determinant of matrix
17394
Sign of determinant when using $det A^\top A$
116376
Prove the determinant is the product of its diagonal entries
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
155537
Intuition of the cyclic trace property of matrix products and relation to the determinant?
121358
What is the exact relation between a full rank matrix and its determinant?
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
75002
show that $\det(A)=0$ in this case