Do Dirac Gamma Matrices act like Tensors?

Do Dirac Gamma Matrices act like Tensors? Is it true that

$$ \gamma_\mu = \eta_{\mu\nu}\gamma^\nu~? $$

Also what about $\sigma_{\mu\nu}$, where $\sigma_{\mu\nu}$ is defined to be: \begin{align*} \sigma_{\mu\nu} = \frac{i}{2}[\gamma_\mu,\gamma_\nu]~? \end{align*}