zeroTwoTwo = DiagonalMatrix[{0,0}]
diracGammaMatrix1 = ArrayFlatten[{{zeroTwoTwo,  PauliMatrix[1]}, {-PauliMatrix[1], zeroTwoTwo}}] 
diracGammaMatrix2 = ArrayFlatten[{{zeroTwoTwo,  PauliMatrix[2]}, {-PauliMatrix[2], zeroTwoTwo}}]
diracGammaMatrix3 = ArrayFlatten[{{zeroTwoTwo,  PauliMatrix[3]}, {-PauliMatrix[3], zeroTwoTwo}}]
diracGammaMatrix4 = DiagonalMatrix[{1,1, -1, -1}]
diracGamma = {{diracGammaMatrix1}, {diracGammaMatrix2}, {diracGammaMatrix3}, {diracGammaMatrix4}} 
FullForm[-I diracGamma[1]]
-I *diracGammaMatrix1  .diracGammaMatrix2. diracGammaMatrix3.  diracGammaMatrix4 //MatrixForm
-I *(diracGamma[1])  .(diracGamma[2]).( diracGamma[3]).  (diracGamma[4]) 

this last line, or the fullform above, doesn't work?

d1 = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0}, {-I, 0, 0, 0}}
d2 = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}
d3 = {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}}
x = I * d1 . d2 
y = x . d3
MatrixForm[y]

z = x * y

a1={{0,-I},{I,0}}
a2={{0,1},{1,0}}
a3={{1,0},{0,-1}}
c=I*a1.a2
MatrixForm[c]
d=c.a3
MatrixForm[d]