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## Homework Statement

Show that [tex]tr(\gamma^{\mu}\gamma^{\nu}\gamma^{5}) = 0[/tex]

## Homework Equations

(anti-)commutation rules for the gammas, trace is cyclic

## The Attempt at a Solution

I can do

[tex] tr(\gamma^{\mu}\gamma^{\nu}\gamma^{5}) = -tr(\gamma^{\mu}\gamma^{5}\gamma^{\nu}) = - tr(\gamma^{\nu}\gamma^{\mu}\gamma^{5}) [/tex]

and so on, but I don't see how that helps me. Any suggestions?