Prove (or disprove) property of determinant: $\;\det(qA) = q^{n} \det(A).$
14646
Prove $\det(kA)=k^n\det A$
63119
Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.
144221
Matrix determinant lemma with adjugate matrix
116376
Prove the determinant is the product of its diagonal entries
17394
Sign of determinant when using $det A^\top A$
87425
Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
20653
Geometric meaning of the determinant of a matrix
106511
Determinant of the sum of matrices: $\det (A + B^T) = \det(A^T + B)$
24873
Determinant of elementary permutation matrix
7205
Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
70092
Determine the number of possible values for $\det(A)$, given that $A$ is an $n \times n$ matrix with real entries such that $A^3 - A^2 -3A +2I=0$.
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$