  We investigate the nearly Gorenstein property of a local ring defined by the
maximal minors of a specific $2 \times n$ matrix with entries in the formal
power series ring $k[[X_1, X_2, \ldots , X_n]]$ over a field $k$. Our findings
allow us to present numerous concrete examples, such as nearly Gorenstein rings
that are not almost Gorenstein and vice versa.
