Proving $adj(A)A=det(A)I$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
7712
How to prove the both identity (matrix)
9574
How to show that $\det(AB) =\det(A) \det(B)$?
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
46669
How can I prove these are the adjoint operators?
23847
Determinant of a matrix whose $(i,j)$th element is $|i-j|$?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
144221
Matrix determinant lemma with adjugate matrix
75855
Show that $\det{(A + sxy^*)}$ is linear in $s$
55018
Prove that $A^*A + I$ is invertible
84775
How to evaluate $\det (1+x_iy_j)_{n\times n}$?