Abstract: We study extreme points of the unit ball of the set of quasi-multipliers of an operator space by introducing the new notion: (approximate) quasi-identities. We give a necessary and sufficient condition for an operator space to become an operator algebra with a contractive approximate quasi- (respectively, left, right, two-sided) identity in terms of extreme points of contractive quasi-multipliers. We also give a necessary sufficient condition for an operator space to become a $C^*$-algebra. Furthermore, we answer the open question about Properties (L) and (R) raised by D. P. Blecher.