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Yes, Ashok Das should strictly speaking not call (2.124) the "inverse set of matrices"; they are only proportional 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 (2.124) is given in (2.126).