How do we know that faith establishes the law?

Paul's argument throughout Romans demonstrates that faith establishes the law by revealing its true purpose. The law was given not as a means to achieve righteousness but to expose our sinfulness and point us to Christ, who fulfills the law. In Romans 7:12, Paul affirms that the law is holy and just, while in Romans 3:20, he states that by the law, we gain the knowledge of sin. Thus, by placing our faith in Christ, we acknowledge the law's demands and affirm that only through Him can we be justified, thereby establishing rather than nullifying the law’s authority.