Abstarct: The purpose of this paper is to provide useful connections between units and zero divisors‎, ‎by investigating the structure of a class of rings in which‎ o the’s ‎conjecture (i.e‎. ‎the sum of two nil left ideals is nil) holds‎. ‎We introduce the concept of unit-IFP for the purpose‎, ‎in relation with the inserting property of units at zero products‎. ‎We first study the relation between unit-IFP rings and related ring properties in a kind of matrix rings which has roles in noncommutative ring theory‎. ‎The Jacobson radical of the polynomial ring over a unit-IFP ring is shown to be nil‎.‎We also provide equivalent conditions to the commutativity via the unit-IFP of such matrix rings‎. ‎We construct examples and counter examples which are necessary to the naturally raised questions.