You mean area factor? (Volume factors are for 3D...)

Think of it this way: if you have an enlargement matrix, say scale factor 2, then your matrix is .

So, if we define a unit square (1x1 length) using four points, say and .

Then if we put all those points into the matrix, the transformed points are and .

These points define a matrix with an area of4square units, so the original unit square got enlarged by an area factor of 4. That is to say, if you used points to define a polygon with area n square units, then the transformed shape will have an area of 4n square units.

For any generic transformation matrix, the area factor is equal to the determinant.

i.e: For any matrix , the area factor is (for a 2x2 matrix).