Yep, another quick question on the Dirac Equation!
I've become slightly more clued about the use of the DE now in illustrating the negative energy problem in relativistic QM as well as the existence of spin, however one thing is still puzzling me.

I've read this excerpt in a text:

I'm not sure I understand how this is proven. Is it something to do with

The Dirac equation should become the Klein-Gordon equation if the DE is multiplied by
[tex]i\gamma_\mu\partial^\mu+m[/tex]. It won't if the gammas commute.