Proof $a+a = 0$ by given $a\times a = a$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
33030
Proof that $\inf A = -\sup(-A)$
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
127296
prove that a|b and b|a iff a=+-b
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
140167
Proving $A+A'B=A+B$ without truth tables
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
32103
Show that for a $2\times 2$ matrix $A^2=0$
66451
In a ring, how do we prove that a * 0 = 0?
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
32929
Questions about proving $\lnot \lnot a = a$