Prove that an element $\bar{x}$ is its own inverse iff $\bar{x} = 1,-1$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
1576
Finding the elements in the group of units of the ring of integers modulo n that are their own inverse.
55018
Prove that $A^*A + I$ is invertible
13136
Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
33355
Proving that matrix in equation is invertible
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
141286
When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
13899
Proof that $-v = (-1)*v$
87289
Find the multiplicative inverses of all the elements in $\Bbb Z_{16}^\times$
112485
Allowing the zero element in a field to have an inverse
106398
If $A$ is invertible show that $\det(A) \neq 0$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
157925
How to prove that the implicit function theorem implies the inverse function theorem?
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
85626
prove $\sum_{i=1}^{n}(x_i-\bar{x})^2\lt\sum_{i=1}^{n}(x_i-a)^2$
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
108589
The inverse of the matrix $\{1/(i+j-1)\}$