Many school textbooks state, but few of them prove, that the determinant of a 2 × 2 matrix is the area scale factor of its transformation; whilst a proof of the corresponding result for 3 × 3 matrices is usually delayed until the scalar triple product is available as a technique. Teachers of SMP, or of other ‘modern’ courses containing some development of transformation geometry, may be interested in the following approach to the topic of determinants.