Show that the characteristic of $R$ is $2$ and that $R$ is commutative.
2709
How to show that every Boolean ring is commutative?
83100
Prove that the center of a ring is a subring.
30794
Commutator Group of $GL_2(R)$ is $SL_2(R)$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
133878
Ring of order $p^2$ is commutative.
60760
Ring homomorphism and characteristic
67990
Commutativity of matrix and its transpose
68065
Quadratic extensions in characteristic $2$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
95513
Proving $W$ is a subspace of $P_{2}$
126429
Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$.
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
133046
Showing $[L,rad(L)]$ is nilpotent.
60140
Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$
45958
Proof that the Euler characteristic is additive
57543
Show that a matrix is nilpotent.