Determinant of a Matrix Proof: $\;\det(qA) = q^n(\det A)$
14646
Prove $\det(kA)=k^n\det A$
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
10083
Determinant of matrix times a constant.
51406
Determinant of a block matrix times the determinant of the inverse of a block
20331
Determinant of a $2\times 2$ block matrix
17394
Sign of determinant when using $det A^\top A$
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
81770
Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
9574
How to show that $\det(AB) =\det(A) \det(B)$?
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
1865
Sub-determinants of an orthogonal matrix
133847
Derivative of determinant of a matrix
20653
Geometric meaning of the determinant of a matrix