  The group structure on the rational points of elliptic curves plays several
important roles, in mathematics and recently also in other areas such as
cryptography. However, the famous proofs for the group property (in particular,
for its associative law) require somewhat advanced mathematics and therefore
are not easily accessible by non-mathematician. On the other hand, there have
been attempts in the literature to give an elementary proof, but those rely on
computer-aided calculation for some part in their proofs. In this paper, we
give a self-contained proof of the associative law for this operation, assuming
mathematical knowledge only at the level of basic linear algebra and not
requiring computer-aided arguments.
