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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).

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.

Yes, Ashok Das should not call (2.124) the "inverse set of matrices." Rather (2.124) is (2.122) where the upper collective index of the 16 matrices (2.122) has been lowered by a metric. 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.

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).

Yes, Ashok Das should not call (2.124) the "inverse set of matrices." Rather (2.124) is (2.122) where the upper collective index of the 16 matrices (2.122) has been lowered by a metric. 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.

Yes, Ashok Das should not call (2.124) the "inverse set of matrices." Rather (2.124) is (2.122) where the upper collective index of the 16 matrices (2.122) has been lowered by a metric. 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.