$(AB)^t = B^tA^t$ for all $A ∈ Mm×k(K)$, $B ∈ M_{k×n}(K)$
20110
How to prove $(AB)^T=B^T A^T$
78307
Under what conditions is $AA^T$ invertible?
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
77667
A and B is similar ⇒ $A^T$ is similar to $B^T$.
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
27738
Gradient of $a^T X b$ with respect to $X$
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues