Proving Gamma 5 Anticommutes with Gamma Matrices

[classy cal]

"It is easily shown" that the gamma 5 matrix anticommutes with the four gamma matrices. Can someone tell me how or provide a link to such proof?

 

[PeterDonis]

You have an equation for $\gamma^5$ in terms of the four gamma matrices. What happens when you write the commutator of $\gamma^5$ and one of the four matrices using that equation?

 

[classy cal]

Thank you Peter. I see now that the order of any two adjacent matrices can be swapped and the sign changed. It is "easy to show". I appreciate you taking the time to point me in the right direction.

 

[PeterDonis]

You're welcome!