Faith is indeed a work and here is some more scripture to demonstrate the point:
1 Thessalonians 1-4
PAUL, SILVANUS, and Timothy, To the church of the Thessalonians in God the Father and the Lord Jesus Christ: Grace to you and peace. We give thanks to God always for you all, constantly mentioning you in our prayers, remembering before our God and Father your work of faith and labor of love and steadfastness of hope in our Lord Jesus Christ. For we know, brethren beloved by God, that he has chosen you;
Rev 2:19
“'I know your works, your love and faith and service and patient endurance, and that your latter works exceed the first.”