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## Homework Statement

Given that [itex]\gamma^{\mu}\gamma^{\nu}+\gamma^{\nu}\gamma^{\mu}=2g^{\mu\nu}*1[/itex] where [itex]1[/itex] is the identity matrix and the [itex]\gamma[/itex] are the gamma matrices from the Dirac equation, prove that:

[itex]\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=2g_{\mu\nu}*1[/itex]

## Homework Equations

[itex]g^{\mu\nu}\gamma_{\nu}=\gamma^{\mu}[/itex] and [itex]g_{\mu\nu}\gamma^{\nu}=\gamma_{\mu}[/itex]

## The Attempt at a Solution

I'm not sure what to start with. I tried expressing the terms of the relation to be proved as follows

[itex]\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=g_{\mu\alpha}\gamma^{\alpha}g_{\nu \beta}\gamma^{\beta}+ g_{\nu\beta}\gamma^{\beta}g_{\mu\alpha}\gamma^{ \alpha }[/itex]

but that isn't going anywhere. So how do I approach this?