Lie Algebra in Particle Physics

In his book " Lie Algebra in Particle Physics" Georgie directly put the relation $$(1-P)D(g)(1-P)=D(g)(1-P)...(1)$$ This came from the two previous relations: $$PD(g)P=D(g)P$$ $$PD(g)P=PD(g).$$ where $$P$$ is the projector and $$D(g)$$ is a representation. How did he conclude relation (1)?

• Just expand (1) and you see it. PS- Georgi is one of the worst books I have ever read. I recommend A. Zee’s book. – Michael Angelo Mar 25 at 9:00
• Thank you! I am yet to finish reading it. A. Zee's book is next on my list. – Sophie Mar 25 at 9:12
• I agree with @MichaelAngelo about Georgi's book, though I must admit I wasn't a huge fan of Zee's book either.. Come to think of it, I'm not even sure how I ever learned group theory.. – InertialObserver Mar 25 at 17:27