In this case A is an adult so he can choose any of the religion he wants. In India from the view point of application of personal laws, it seems, a person neither can belong to two religions nor be without any religion. In India, unless a person converts to another religion, he continues to belong to his community of origin or birth.
According to Hindu Law a person will be Hindu by birth if one of his parents at the time of his birth was a Hindu and brought up as a Hindu . In case of Muslim law, according to the Shariat, if one parent is Muslim, the Child will be Muslim. Therefore, we can see that under Hindu Law, if one of the parents is a Hindu and the other is Muslim, and if the child is brought up as a Hindu, the child will be Hindu . The rule of Muslim Law, it is submitted, will be subject to this rule of Hindu Law . Generally, in the cases of divorce between parents this question arises, but when the child is minor it depends on the welfare of the children.
In my view, it is solely dependent on A which religion he likes to profess as he is an adult and has freedom to choose among both the religions.

References:

Myna Boyce v. Octaram, (1961)8 MIA 400;
Ram Prakash v. Debnab, ILR (1942) Pat 152;
Vennamuddals v. Cherhati, AIR 1953 Mad. 571
Paras Diwan, Family Law, 10th Edn. Allahabad Law Agency, 2013. Pgs: 5-7

At the age of 18, A has the choice of either following Hinduism or Islam.
Generally, the religion of the child is determined and mentioned at the time of birth in the Birth Registration Certificate. However if the parents follow different religion, then the religion of the child is determined by the practices followed by the parents while bringing up the child. Over a long period of time, the patriarchal system of our society demanded that the religion of the father is devolved to the child but that is not a legal mandate. Moving to the Muslim personal law practiced in India, a child of Muslim parents is a Muslim while if the father is a Muslim then under the Muslim law there is a presumption that the child is a Muslim unless proved otherwise.
Under the Muslim Personal Law (Shariat) Application Act, 1937, person needs to make a declaration that he is a Muslim, and such a declaration has to be substantiated. A person is said to be a Muslim when he believes, a) in the unity of God i.e. Allah, and b) that Mohammed is the prophet of Allah. This definition, in essence, tells us that a Muslim is just that man who believes in the oneness of Allah and believes in Mohammed being his prophet. Therefore, to remove the presumption that A is a Muslim, A must avoid making such a declaration and show that he does not consider Mohammed as the prophet of Allah to indicate that he should not be considered as a Muslim by virtue of his father’s religion.
In the present situation given in the question, the father is a Muslim therefore there is a strong presumption of the fact that A will be considered as a Muslim. However, A also has the option to prove that he is not a Muslim and follow Hinduism instead.
Therefore depending upon the general presumption of Muslim law he will be considered as a Muslim and the Muslim law will apply if he marries a Muslim girl or the Special Marriage Act will apply if A marries a non-Muslim girl. Where he can prove substantially that he is not a Muslim as per the requirement of Muslim law and can decide his religion as per his choice which will determine the personal law governing hi marriage.

References:
Article 25 of the Constitution of India, S.R. Bommai v. Union of India (1994 (3) SCC 1)
Maneka Gandhi v. Indira Gandhi, AIR 1985 Del 114 ( A part of case deals with succession and determination of religion)
Family Law lectures, Poonam Pradhan Saxena, 3rd Edition, LexisNexis Student Series
Bhagwan Baksh v. Digbijai Singh, ILR 1931 6 Oudh 487
Bhaiya sher Bahadur v. Bhaiya Ganaga Baksh Singh, (1914)41 IA L
Muslim Law in Modern India ,Dr. Paras Diwan,10th edition, 2011 reprint 2012, Jain Book Agency.