$\text{det}(I-AB)=\text{det}(I-BA)$
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
24873
Determinant of elementary permutation matrix
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
10083
Determinant of matrix times a constant.
69641
Determinant identity: $\det M \det N = \det M_{ii} \det M_{jj} - \det M_{ij}\det M_{ji}$
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
84775
How to evaluate $\det (1+x_iy_j)_{n\times n}$?
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
133756
Geometric interpretation of $\det(A^T) = \det(A)$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
123555
Proving that if $ab=e$ then $ba=e$
12355
Sylvester's determinant identity
40538
On determinants and common divisors
101040
Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
151526
Determinant of a matrix with different cases for its entries
75002
show that $\det(A)=0$ in this case
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$