$ax=0$ if and only if $a=0$ or $x=0$
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
140252
Matrices - Conditions for $AB+BA=0$
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
33469
Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$
153272
Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
8360
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$
1102
Way to determine if X and Y are both over 0
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
73677
If the matrix $A^3 = 0$, is $A$ singular?
55820
If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
110408
Solving for $A$ in $Ax = b$
77764
Is "$a + 0i$" in every way equal to just "$a$"?
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$