I was reading Steven Simon's notes on Topology to understand few ideas used in condensed matter theory. I want to declare that I don't have any formal knowledge of knots and topology in general. So when I was reading the chapter 2, where he explains the rules to get Kauffman invariant, I got it for the worked out examples. But on page 13 while explaining the knot in single string with open boundary, he asks to think of it as a ribbon. Then he equates the twisted ribbon to $-A^{3}$ times ribbon without any twist. Link to image here.
How do I get that? I couldn't get it using the rules he mentioned earlier in the chapter. Am I doing something wrong?
Thanks in advance.