Yes, Ashok Das should strictly speaking not call (2.124) the "inverse set of matrices"; they are only proportional$^1$ to the inverse. Rather (2.124) is (2.122) where the upper collective index $(a)$ of the 16 matrices (2.122) has been lowered by a metric $g_{(a)(b)}$. The (inverse) metric is here defined as 
$$g^{(a)(b)}~:=~ {\rm Tr}(\Gamma^{(a)}\Gamma^{(b)}), \qquad a,b~\in~\{1,\ldots,16\},\tag{2.123}$$
which is diagonal. The explicit list of $\Gamma_{(a)}$ is given in (2.126).

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$^1$ It is straightforward to check this explicitly by going through the list.