Is zakat obligatory on a house owned by its owner and inhabited by others in exchange for rent paid by the house's owner to rent another house for himself at the same value?

A house designated for rent is not subject to zakat. Zakat is only obligatory on the rental income derived from it, provided that it reaches the nisab (minimum threshold) and a hawl (one lunar year) passes over it, with the condition that it is not spent before the end of the hawl.