query: Is it true that if $|A|>\frac{|G|}{2}$ then $A^{-1}A=AA^{-1}=G$?
positive_passages.docid: 58654
positive_passages.text: If $|A| > \frac{|G|}{2} $ then $AA = G $
negative_passages.docid: 57421
negative_passages.text: If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
negative_passages.docid: 43453
negative_passages.text: Is ${\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^\sqrt2}}}}^{...}=4$ correct?
negative_passages.docid: 83662
negative_passages.text: Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
negative_passages.docid: 68705
negative_passages.text: Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
negative_passages.docid: 158862
negative_passages.text: Show that $a(-1) = (-1)a = -a $.
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 101491
negative_passages.text: If $\frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|}$, then why is $\frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}=0$?
negative_passages.docid: 60900
negative_passages.text: If $A^2=-I$, Prove that $\det{A}=1$
negative_passages.docid: 38404
negative_passages.text: Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
negative_passages.docid: 149553
negative_passages.text: Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
negative_passages.docid: 83938
negative_passages.text: If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
negative_passages.docid: 73391
negative_passages.text: Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
negative_passages.docid: 90486
negative_passages.text: If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
negative_passages.docid: 147014
negative_passages.text: Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
negative_passages.docid: 85984
negative_passages.text: How come $\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} = g_{\beta\mu}g_{\gamma\nu}$?
negative_passages.docid: 72906
negative_passages.text: Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?