二、民法第一條:「民事，法律所未規定者，依習慣；習慣者，依法理。」請從法律思想變遷與相關法理學派發展角度說明此條的立法原理(50%)

3. [20%] Prove the following simple form of the structure theorem for finitely generated mod- ules over a principal ideal domain (so you ca can not apply the struc cture theo orem directly). Let A be a principal ideal domain and M a 2 x 2 matrix whose entries are in A. Show that there exist invertible matrices P, Q with entries in A and a,β A with a | β such that