Prove that $\det (E + h A) = 1 + h \operatorname{tr} A + O(h^2)$ for $h \to 0$
131408
Find the expansion for $\det(I+\epsilon A)$ where $\epsilon$ is small without using eigenvalue.
149086
Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
38850
How to show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
109099
Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
9574
How to show that $\det(AB) =\det(A) \det(B)$?
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
85872
Prove $1 + \tan^2\theta = \sec^2\theta$
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
60900
If $A^2=-I$, Prove that $\det{A}=1$
128723
The determinant of adjugate matrix
133756
Geometric interpretation of $\det(A^T) = \det(A)$
71442
How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$