# Determinant of matrix with unit length rows

What can be said about the determinant of a matrix when its rows (or similarly, columns) are unit vectors?

Do such determinants have a geometric interpretation? For example, in the two-dimensional case, the determinant of two unit length vectors is the sinus between them.

If the rows or columns of a matrix $M$ are unit vectors (in the usual Euclidean norm), then $\det M\le 1$.
One geometric interpretation of the determinant is the (signed) volume of the parallelotope ($n$-dimensional generalization of the parallelepided) spanned by the column vectors or row vectors of the matrix.