  In this paper we investigate the question of when the determinantal ring $R$
over a field $k$ is an almost Gorenstein local/graded ring in the sense of
Goto, Takahashi, and the author. As a consequence of the main result, we see
that if $R$ is a non-Gorenstein almost Gorenstein local/graded ring, then the
ring $R$ has a minimal multiplicity.
