Let $A, B, C$ be some complex matrices. If $AB - BA = C$ and $AC = CA$, then $C^k = 0$ for some $k$.
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
82410
Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
43570
Finding two non-zero matrices where $AX = BA$
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
120867
How prove this two symmetric matrices $AB=0$
110502
$AB=BA$ with same eigenvector matrix
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
78755
If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?