Both Jewish Christians and many Gentile Christians were familiar with the law. Jewish people were taught the law of Moses from birth. Many Gentiles in the church at Rome had previously been God-fearers. These were Gentiles who were interested in Judaism and regularly attended the synagogue.
the law has authority over a man only as long as he lives: Paul might be referencing a well-known Jewish saying. One rabbinic tradition says, “If a person is dead, he is free from the Torah and the fulfilling of the commandments” (Babylonian Shabbat 30a; baraita Shabbat 151).