What is the ruling on buying a car in installments from a dealership and selling it for cash to another person without transferring its ownership to me, where the buyer directly transfers ownership from the dealership, in order to obtain liquidity and pay the monthly installments, and is it permissible to sell the car back to the same dealership after buying it from them in installments?

The first scenario: Buying a car with a deferred payment, then selling it to a third party other than the showroom for immediate payment, even if for less than the purchase price, without registering its ownership in your name, is permissible. This type of transaction is known as "Tawarruq," and there is no harm in it, provided that the commodity enters into the possession and guarantee of the buyer.

The second scenario: Selling the car to the same showroom from which you bought it, for cash and at a lower price, is not permissible, because it falls under the prohibited "Bay' al-'Inah" (buy-back sale).