If $AB = BA$ for $A,B \in \mathcal{L}(V,V)$, then $A$ and $B$ have these properties
58572
Prove two commutative linear transformations on a vector space over an algebraically closed field can be simultaneously triangularized
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
55062
$2\times 2$ matrix $C=AB-BA$
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
15626
Relations of a~b iff b = ak^2