Is $\det(AB) = \det(A)\det(B)$ for entries in commutative ring?
9574
How to show that $\det(AB) =\det(A) \det(B)$?
40538
On determinants and common divisors
154581
Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
87425
Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
517
Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$)
14646
Prove $\det(kA)=k^n\det A$
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
25713
If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$.
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
106619
Determinant of matrix
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
22215
How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
132317
linear algebra over a division ring vs. over a field