If $x^2 a x=a^{-1}$, then $a$ has a cube root.
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
108633
Why $f^{-1}(f(A)) \not= A$
130799
Matrix of rank 1; show that $A^2=cA$ for some scalar $c$.
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
115296
Under what conditions does a matrix $A$ have a square root?
92701
let $a,b,c \in\mathbb{R} ,a<3$ and all roots $p(x)=x^3+ax^2+bx+c=0$ be negative . then prove that $b+c\neq 4$
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
80229
How to prove this curiosity that has to do with cubes of certain numbers?
60900
If $A^2=-I$, Prove that $\det{A}=1$
83363
Finding the real root of a cubic algebraically
80304
Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers
15730
Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
5410
Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
75503
Rationalizing a Denominator with Cube Roots