Is faith a work

Romans 4:5

But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.

In the above scripture we see that the person who has faith, who believes, is not performing a work. Thus, faith is not a work.

Romans 9:32

Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;

We see in Romans 9:32 that works are not faith.