c is a general associative, but non-commutative, form of multiplication.
NonCommutativeMultiply has attribute Flat.
Instances of NonCommutativeMultiply are automatically flattened, but no other simplification is performed.
You can use NonCommutativeMultiply as a generalization of ordinary multiplication for special mathematical objects.
See the Mathematica book: Section A.2.7.
See also: Dot, Times, Cross.
Multiplication is a commutative operation.
But the noncommutative operator ** does not have this property.
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