 Solution

The gamma matrices represent the spacetime Clifford algebra. With the Minkowski metric convention above,The braces denote the anticommutator. Consequently $({\gamma }^0{)}^2=I_4$, $({\gamma }^i{)}^2=-I_4$, and distinct gamma matrices anticommute. The identity matrix is essential: the right side is a matrix equality, not a scalar equality. These signs agree with the explicit Dirac representation of the gamma matrices in the next part.