If $A^2=A$, $B^2=B$ and $I-(A+B)$ is invertible, then $R(A) = R(B)$
37162
Prove that matrices have equal rank.
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
69160
Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
145397
How to prove that for every $i$, $a_i = i$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
69509
Showing a Linear Transformation is invertible
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect