Cross simplification property: does ax=ya $\Rightarrow$ x=y implies conmutativity?
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
93952
Show that $X$ can be represented as a union of disjoint equivalence classes
102383
Associativity of Cartesian Product
140190
Binary operation $xy$, has identity, but not associativity. Is the inverse unique?
87451
Construction of matrices under ZFC axioms
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
146231
Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.
137921
Reflexivity, Transitivity, Symmertry of the square of an relation
28003
How to prove $A+ A^T$ symmetric, $A-A^T$ skew-symmetric.
102418
Rotations preserve cross products?
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
58572
Prove two commutative linear transformations on a vector space over an algebraically closed field can be simultaneously triangularized
24139
Logical explanation why exponentiation operation is not commutative and associative
143646
Is it possible to prove reflexive, symmetric and transitive properties of equality and the transitive property of inequality?
74377
Is the natural order relation on an idempotent semiring total/linear?
72551
Proof that $\rho = \pm1$ implies linear combination