DeclareNonCommutative[a, b, ...] declares a,b, ... to be non-commutative, i.e., DataType[a,b, ..., NonCommutative] is set to True.
Overview, DataType, UnDeclareNonCommutative.
As a side effect of DeclareNonCommutative, x is declared to be of data type NonCommutative.
DeclareNonCommutative[x]DataType[x, NonCommutative]\text{True}
DeclareNonCommutative[y, z]
DataType[a, x, y, z, NonCommutative]\{\text{False},\text{True},\text{True},\text{True}\}
UnDeclareNonCommutative[x, y, z]
DataType[a, x, y, z, NonCommutative]\{\text{False},\text{False},\text{False},\text{False}\}