Diagrams described by this property are studied in category theory, and the SO(3) group representing the set of rotations in 3-space lacks this property.
In linear algebra, sets of linear transformations that share a common eigenbasis necessarily have this property. Diagrams described by this property are studied in category theory, and the SO(3) group representing the set of rotations in 3-space lacks this property. Groups that have this property are called (*) abelian, and the cross-product has the "anti" form of this property wherein the result is negated. This property does not always hold for matrix multiplication or division, but it does for addition and multiplication, since order in those operations does not matter. For 10 points, name this property that can be stated as a times b equals b times a.
In linear algebra, sets of linear transformations that share a common eigenbasis necessarily have this property.
commutative (accept word forms; accept abelian before read)