Prove each of the identities: (gamma^{mu} sigma^{ho sigma} gamma_{mu}=0, sigma^{mu u} sigma_{mu u}=12, gamma^{mu} sigma^{ho sigma} gamma^{lambda}

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Prove each of the identities: \(\gamma^{\mu} \sigma^{ho \sigma} \gamma_{\mu}=0, \sigma^{\mu u} \sigma_{\mu u}=12, \gamma^{\mu} \sigma^{ho \sigma} \gamma^{\lambda} \gamma_{\mu}=2 \gamma^{\lambda} \sigma^{ho \sigma}\), \(\gamma^{\mu} \gamma^{\lambda} \sigma^{ho \sigma} \gamma_{\mu}=2 \sigma^{ho \sigma} \gamma^{\lambda}, \sigma^{\mu u} \gamma^{ho} \sigma_{\mu u}=0, \sigma^{\mu u} \gamma^{ho} \gamma^{\sigma} \sigma_{\mu u}=4\left(4 g^{ho \sigma}-\gamma^{ho} \gamma^{\sigma}\right)\) and \(\sigma^{\mu u} \sigma^{ho \sigma} \sigma_{\mu u}=\) \(-4 \sigma^{ho \sigma}\).

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