= Solution
Use $\hbar=c=1$ and the <Minkowski metric> $\eta=\operatorname{diag}(1,-1,-1,-1)$ throughout. In the four-component <Dirac spinor> representation, the <gamma matrices> generate the <Clifford algebra>
$$
\boxed{\{\gamma^\mu,\gamma^\nu\}=\gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu=2\eta^{\mu\nu}I_4.}
$$
Thus $(\gamma^0)^2=I_4$, $(\gamma^i)^2=-I_4$, and matrices with distinct indices anticommute. Indices are lowered with $\eta$, so $\gamma_\mu=\eta_{\mu\nu}\gamma^\nu$ and $\not p=p_\mu\gamma^\mu$.
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