  In this paper we give a comparison between the formulation of the concept of
metric for a real vector space of finite dimension in terms of \emph{tensors}
and \emph{extensors}. A nice property of metric extensors is that they have
inverses which are also themselves metric extensors. This property is not
shared by metric tensors because tensors do \emph{not} have inverses. We relate
the definition of determinant of a metric extensor with the classical
determinant of the corresponding matrix associated to the metric tensor in a
given vector basis. Previous identifications of these concepts are equivocated.
The use of metric extensor permits sophisticated calculations without the
introduction of matrix representations.
