query: Why do we have $ab=ba$?
positive_passages.docid: 5893
positive_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 157087
negative_passages.text: Can anyone explain why $a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$
negative_passages.docid: 34973
negative_passages.text: Is it true that the order of $ab$ is always equal to the order of $ba$?
negative_passages.docid: 43570
negative_passages.text: Finding two non-zero matrices where $AX = BA$
negative_passages.docid: 13346
negative_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 92377
negative_passages.text: Why is $\mathbf{B}$ a pseudovector?
negative_passages.docid: 37061
negative_passages.text: The order of $ab$ when $a,b$ commute
negative_passages.docid: 33542
negative_passages.text: When is $A- B = B- A$?
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 153290
negative_passages.text: $A^TA=B^TB$. Is $A=QB$ for some orthogonal $Q$?
negative_passages.docid: 25682
negative_passages.text: If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 45760
negative_passages.text: if G is generated by {a,b} and ab=ba, then prove G is Abelian
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 56097
negative_passages.text: If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?
negative_passages.docid: 129007
negative_passages.text: Relation between AB and BA