The absolute value of a $2 \times 2$ matrix determinant is the area of a corresponding parallelogram with the $2$ row vectors as sides.

The absolute value of a $3 \times 3$ matrix determinant is the volume of a corresponding parallelepiped with the $3$ row vectors as sides.

Can it be generalized to $n-D$? The absolute value of an $n \times n$ matrix determinant is the volume of a corresponding $n-$parallelotope?