How to prove $\det \begin{bmatrix}A & B \\ C & D \end{bmatrix} =\det(AD-BC)$, where $A, B, C,$ and $D$ are $n\times n$ and commuting.
72326
Determinant of block matrix with commuting blocks
29568
Prove that the determinant of $ A^{-1} = \frac{1}{det(A)} $- Linear Algebra
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
4998
Question on determinants of matrices changing between integer matrices
67990
Commutativity of matrix and its transpose
57027
Determinant of this skew symmetric matrix
101631
Determinant of a finite-dimensional matrix in terms of trace
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
55062
$2\times 2$ matrix $C=AB-BA$
23847
Determinant of a matrix whose $(i,j)$th element is $|i-j|$?
155537
Intuition of the cyclic trace property of matrix products and relation to the determinant?
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
517
Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$)