$\det\left[ \begin{matrix} A & B \\ B & A \end{matrix} \right] \ = \ \det\left( A + B \right) \det( A - B )$ for $AB \neq BA$
109312
How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
141173
Are there matrices such that $AB=I$ and $BA \neq I$
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
107128
Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
12355
Sylvester's determinant identity
9574
How to show that $\det(AB) =\det(A) \det(B)$?
31999
Relation of this antisymmetric matrix $r = \left(\begin{smallmatrix}0 &1\\-1&0\end{smallmatrix}\right)$ to $i$
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
14646
Prove $\det(kA)=k^n\det A$
142640
Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
110502
$AB=BA$ with same eigenvector matrix
55062
$2\times 2$ matrix $C=AB-BA$
66709
Are the matrix products $AB$ and $BA$ similar?
79031
Determinant of the Kronecker Product of Two Matrices
29568
Prove that the determinant of $ A^{-1} = \frac{1}{det(A)} $- Linear Algebra