You really need to stop grabbing a verse of scripture in isolation, you will not understand the context if you do:
Romans 3:31, that verse is part of a much larger section of verses. Reading a verse in isolation, without verses associated with it, can give a misleading understanding of the verse:
Therefore no one will be declared righteous in God’s sight by the works of the law; rather, through the law we become conscious of our sin.
21 But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify.
22 This righteousness is given through faith inh]">[h] Jesus Christ to all who believe. There is no difference between Jew and Gentile,
23 for all have sinned and fall short of the glory of God,
24 and all are justified freely by his grace through the redemption that came by Christ Jesus.
25 God presented Christ as a sacrifice of atonement,i]">[
i] through the shedding of his blood—to be received by faith. He did this to demonstrate his righteousness, because in his forbearance he had left the sins committed beforehand unpunished—
26 he did it to demonstrate his righteousness at the present time, so as to be just and the one who justifies those who have faith in Jesus.
27 Where, then, is boasting? It is excluded. Because of what law? The law that requires works? No, because of the law that requires faith. 28 For we maintain that a person is justified by faith apart from the works of the law. 29 Or is God the God of Jews only? Is he not the God of Gentiles too? Yes, of Gentiles too,
30 since there is only one God, who will justify the circumcised by faith and the uncircumcised through that same faith. 31
Do we, then, nullify the law by this faith(righteousness of faith)? Not at all! Rather, we uphold the law. 20-31
In the above section, of which verse 31 is included, Paul states no one will declared righteous in God’s sight by works of the law/obeying the law. Believers have a righteousness apart from law. A believer’s righteousness is faith in Christ. Boasting is excluded, because a person is not justified/righteous by law but by faith(in Christ) apart from the law.
Now what would many of Paul’s readers have thought when reading the above? The same as many on this website it seems would think. ‘
Well if we have righteousness apart from the law, we can act however we like, and ignore the good and Holy laws of God.’ And so, Paul, knowing many would come to that conclusion, finished the chapter with verse 31
Paul’s view was the complete opposite of what many believe. To him, if you live by a righteousness of faith in Christ, not one of obeying the law, you will not nullify, or make void the law, but rather you will uphold it, or establish it.
So to accept Paul’s message concerning this subject, two questions need to be asked
1) Why, if a believer has no righteousness of obeying the law is this not a licence to sin?
2) Why, if you live under a righteousness of faith in Christ, rather than one of obeying the law, will this result in you upholding, or establishing the law?