Inverse of $1-ba$ when $a,b$ are the elements of unital algebra $A$
83255
Finding inverse in non-commutative ring
57846
Multiplicative inverse in $\operatorname{GF}(2^8)$?
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
131701
Why is $A^TA$ invertible if $A$ has independent columns?
112485
Allowing the zero element in a field to have an inverse
87946
Proving that the unities of a ring form a group under multiplication
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
147332
A finite von Neumann regular ring is unital and has $ab = 1$ if $ba = 1$
42941
Pair of adjoint functors and showing that two certain maps are inverses
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
24499
Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
1576
Finding the elements in the group of units of the ring of integers modulo n that are their own inverse.