  We introduce the key concepts of duality mappings and metric extensor. The
fundamental identities involving the duality mappings are presented, and we
disclose the logical equivalence between the so-called metric tensor and the
metric extensor. By making use of the duality mappings and the metric extensor,
we construct the so-called metric products, i.e., scalar product and contracted
products of both multivectors and multiforms. The so-known identities involving
the metric products are obtained. We find the fundamental formulas involving
the metric extensor and, specially, we try its surprising inversion formula.
This proposal unveils, once and for all, an unsuspected meaning of the metric
products.
