I am looking for the general problem class / computational complexity / algorithms for the following problem:

*N tasks must be accomplished by N persons. 1 task to be done by exactly 1 person and vice versa. There is a binary preferences matrix whose (i,j) entry is 0 if person i can not do task j, and 1 if it can.*

There are no costs involved, no weights and the number of tasks equals the number of people.

I was searching for it but all I could find was the Assignment Problem which has costs/weights associated with each assignment.

As a last resort, perhaps I can transform my preferences matrix to a cost matrix if person can not do job then cost is infinite else cost is zero?