As is well known, the Hadamard inequality is trivial from this point of view. But the Hadamard inequality is discovered so late.
According to O'Connor and Robertson, the first observation dates 250 years ago:
Lagrange, in a paper of 1773, studied identities for 3 × 3 functional determinants. However this comment is made with hindsight since Lagrange himself saw no connection between his work and that of Laplace and Vandermonde. This 1773 paper on mechanics, however, contains what we now think of as the volume interpretation of a determinant for the first time. Lagrange showed that the tetrahedron formed by $O(0,0,0)$ and the three points $M(x,y,z)$, $M'(x',y',z')$, $M''(x'',y'',z'')$ has volume $$\frac16 [z(x'y'' - y'x'') + z'(yx'' - xy'') + z''(xy' - yx')].$$