  In the present paper we prove that every 2-local inner derivation on the
matrix ring over a commutative ring is an inner derivation and every derivation
on an associative ring has an extension to a derivation on the matrix ring over
this associative ring. We also develop a Jordan analog of the above method and
prove that every 2-local inner derivation on the Jordan matrix ring over a
commutative ring is a derivation.
