In a group if $ab=e$ then is it always true that $ba=e$?
123555
Proving that if $ab=e$ then $ba=e$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
117538
What is the interpretation of $a \equiv b$ mod $H$ in group theory?
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
131844
When does $(e^a)^b = e^{ab}$ hold?
33542
When is $A- B = B- A$?
110672
Is it true that $aH = bH$ iff $ab^{-1} \in H$
18800
If A and B are symmetric is AB=BA true?
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
120573
Does $a!b!$ always divide $(a+b)!$
29051
If I know the order of every element in a group, do I know the group?
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian