  Gram determinants earned traction among knot theorists after E. Witten's
presumption about the existence of a 3-manifold invariant connected to the
Jones polynomial. Triggered by the creation of such an invariant by N.
Reshetikhin and V. Turaev, several mathematicians have explored this line of
research ever since. Gram determinants came into play by W. B. Raymond
Lickorish's skein theoretic approach to the invariant. The construction of
different bilinear forms is possible through changes in the ambient surface of
the Kauffman bracket skein module. Hence, different types of Gram determinants
have arisen in knot theory throughout the years; some of these determinants are
discussed here. In this article, we introduce a new version of such a
determinant from the M\"obius band and prove some important results about its
structure. In particular, we explore its connection to the annulus case and
factors of its closed formula.
