Did Paul keep the law?

I just came across a scripture that I think answers the question. According to I Corinthians 9:19-23, Paul did keep the law even though he considered himself not under the law. Even among the Gentiles, Paul kept the law since there were always Jews around. He also kept the completed(fulfilled)law in Christ Jesus.

I Corinthians 9:19-"For though I am free from all men, I have made myself a slave to all, that I might win the more. 20 To the Jews I became as a Jew, in order to win Jews; to those under the law I became as one under the law—though not being myself under the law—that I might win those under the law. 21 To those outside the law I became as one outside the law—not being without law toward God but under the law of Christ—that I might win those outside the law. 22 To the weak I became weak, that I might win the weak. I have become all things to all men, that I might by all means save some. 23 I do it all for the sake of the gospel, that I may share in its blessings."