  We construct a basis for the right quantum algebra introduced by
Garoufalidis, Le and Zeilberger and give a method making it possible to go from
an algebra submitted to commutation relations (without the variable q) to the
right quantum algebra by means of an appropriate weight-function. As a
consequence, a strong quantum MacMahon Master Theorem is derived. Besides, the
algebra of biwords is systematically in use.
