Let a be a matrix of order m * n, and the rank of a is equal to m and less than N. why is the determinant of (transpose of a multiplied by a) equal to zero

Let a be a matrix of order m * n, and the rank of a is equal to m and less than N. why is the determinant of (transpose of a multiplied by a) equal to zero

Knowledge point: determinant of n-order square matrix A is equal to 0 R (a)

Is there a matrix with full rank whose determinant operation value equals zero?

Full rank of square matrix A
A reversible
|A|≠0

If the rank of matrix is r, is it possible to have a determinant of r-order subexpression equal to 0
Because the definition only says that there is one, but there can be several r-order subexpressions. Is it possible that some cases equal to 0 and some cases not equal to 0 exist at the same time? Why

If the rank of a matrix is r, there may be a determinant of a r-order subformula equal to 0, several r-order subformulas, or some equal to 0 and some not equal to 0