In Italy, Theorem 1.4 is known as Binet Theorem after Jacques Philippe
Marie Binet (1786-1856). Theorem 1.4 is in fact a special case of the Cauchy Binet formula concerning the determinant of the product of two rectangular
matrices of transpose shapes (see, for instance, Proposition 3.4 in [21]).
We end this section by recalling the renowned condition for the existence
of a solution to a system of linear equations.