Along with distributivity, matrix multiplication possesses this property.
The Moufang identities closely resemble this property, but they do not imply it. If the subalgebra generated by any element of an algebra has this property, the algebra has the "power" form of this property. A magma with this property is a semigroup. The octonions lack this property, but the quaternions and the complex numbers possess it. An algebraic structure that possesses an (*) identity element, an inverse element, closure, and this property is a group. Along with distributivity, matrix multiplication possesses this property. For 10 points, name this property of a binary operation which for multiplication means quantity ab times c equals a times quantity bc.
The Moufang identities closely resemble this property, but they do not imply it.
associativity [or associative, do not under any circumstances accept or prompt on "associated with"]