Is it permissible for me to give rides to women in my car, whether they are elderly or of my wife's age, to help them with transportation?

There is no منع (prohibition) for women, especially elderly women, to ride in a car with a non-mahram (definition) man if he is accompanied by others, as long as there is no fear of temptation (fitna) and no physical contact. However, if he is alone, it is not permissible for a non-mahram woman to ride with him unless there is a necessity or an urgent need, due to the absence of someone who would negate the state of khalwa (definition) (private seclusion).