The answer is “NO”. The determinant only exists for square matrices.

Can a matrix have no determinant?

Math 21b: Determinants. The determinant of any square matrix A is a scalar, denoted det(A). [Non-square matrices do not have determinants.] … In particular, if any row or column of A is zero then det(A)=0; if two rows or two columns are proportional, then again det(A)=0.

Which matrices can have determinants?

For a square matrix, i.e., a matrix with the same number of rows and columns, one can capture important information about the matrix in a just single number, called the determinant.