Prove $\det(e^{tA})=e^{t\cdot{tr} (A)}$
53917
Determinant of matrix exponential?
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
14646
Prove $\det(kA)=k^n\det A$
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
36090
$TT^*=T^2$, show that $T$ is self-adjoint
118996
Prove that $T$ is an orthogonal projection
130253
Differentiating $\mbox{tr} (ABA^TC)$ w.r.t. $A$
18282
Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
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 $\det(AA^T)=nk^2.$
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
29568
Prove that the determinant of $ A^{-1} = \frac{1}{det(A)} $- Linear Algebra
22215
How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
46825
The identity det(A) = exp(Tr(ln(A)) for A general
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$