Is it permissible for a merchant to take money from his mother and paternal aunt to invest it and provide housing and a monthly salary for them, knowing that he takes care of his mother even if she owns nothing, and his aunt has no children and is in the position of a divorcee?

It is a condition for investing money through Mudarabah (definition) (profit-sharing) that both parties agree on a common, undivided share of the profit. It is not permissible to stipulate a fixed amount or a percentage of the capital. If one of the partners stipulates a known number of dirhams, the partnership becomes void by consensus. Therefore, Mudarabah is not permissible with your mother's and aunt's money in exchange for providing housing and a known salary. Rather, an agreement must be reached on a percentage of the profit, and any loss will be borne by them in proportion to their capital. After agreeing upon the Sharia (definition)-compliant conditions, there is no objection to donating a residence or a salary to them. If the mother is poor, her maintenance, including providing housing, becomes obligatory upon the son.