The paper studies the problems of stabilization and pole placement in linear multi-variable systems by means of unity rank output feedback matrices. The results are given in the form of two lemmas : the Stabilization lemma and the Pole placement lemma. These lemmas give two simple necessary conditions for the existence of a stabilizing feedback matrix and a feedback matrix which places the poles at arbitrary locations. The conditions are given in terms of the coefficients of the system transfer-function matrix and are illustrated by a number of numerical examples.