query: Relationship between $\operatorname{ord}(ab), \operatorname{ord}(a)$, and $\operatorname{ord}(b)$
positive_passages.docid: 25713
positive_passages.text: If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$.
negative_passages.docid: 118310
negative_passages.text: How to find $\operatorname{Gal}(S/\mathbb{Q})$
negative_passages.docid: 97767
negative_passages.text: How do I construct a function $\operatorname{sog}$ such that $\operatorname{sog}\circ\operatorname{sog} = \log$?
negative_passages.docid: 130620
negative_passages.text: Identity type between A and B being non-empty implies non-emptiness of A and B?
negative_passages.docid: 100844
negative_passages.text: How should I understand "$A$ unless $B$"?
negative_passages.docid: 39646
negative_passages.text: Is there a relation between $\rho(A) + \rho(B)$ and $\rho(A+B)$, where $\rho$ is the spectral radius?
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 57055
negative_passages.text: Are $|X|$ and $\operatorname{sgn}(X)$ independent?
negative_passages.docid: 131212
negative_passages.text: Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 13020
negative_passages.text: Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$?
negative_passages.docid: 95928
negative_passages.text: Independence and orthogonality
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 128673
negative_passages.text: Given $A : \mathcal{C} \rightarrow \mathcal{E}$, when does $\operatorname{colim} A = A(1)$?
negative_passages.docid: 28565
negative_passages.text: Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
negative_passages.docid: 104653
negative_passages.text: $A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?