Here is the question:
Show that if L is a left ideal of the ring M2(F), F any field, then L consists of all left multiples of some element A in M2(F).
Show that this A can be chosen to be idempotent, such that A^2=A.
Show that the foregoing assertions hold not just for M2(F) but also for Mn(F), any n.
Any help would be great!