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What term describes the property of terms that can be multiplied or divided in any order?

ie, xyz = yxz

or x+y+xy+c = c+x+y+yx

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    It is the commutative peoperty of addition and multiplication of ( I assume you're working with) real numbers.2011-11-09
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    Please write that as an answer, @gary.2011-11-10
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    @J.M: thanks for the reminder.2011-11-10

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The property that describes the fact that the order in which a sum or product is done does not affect the outcome of the sum or product is called the commutative property, and the property may extend to all sorts of different operations, like group multiplication (in Abelian groups, of course).

EDIT: Notice that commutativity does not always hold; as an example, consider multiplication of matrices in the set of all $n\times n$ matrices with entries in (for definiteness) the reals, in which the only matrices that commute with all other scalar matrices are the matrices that are scalar multiples of the identity, i.e., matrices of the type $cI$ , where $c$ is a real scalar, and $I$ is the identity See e.g this link. Still, there are subsets of the set of all matrices with real entries that commute with each other under multiplication, like rotation matrices (with all rotations done about the same axis of rotation). The fact that these matrices commute is a reflection of the fact that rotating (again, fixing the axis of rotation) first by an angle $\theta$ and then by $\alpha$ is equivalent to rotating first by $\alpha$ and then by $\theta$.

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    Presumably what you meant was that a matrix commutes with everything if and only if its a scalar multiple of the identity matrix.2011-11-10
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    @Alex: yes, that is what I meant; let me edit it.2011-11-10
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    What is the axis of rotation of a rotation matrix in dimension other than 3?2011-11-10
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    @Didier:I know the situation is more complicated then, but I don't know enough. Let me edit to mention that I'm referring to the case n=3; would that do it?2011-11-10