In the book "String theory and M-theory" by Becker-Becker-Schwarz, the author says that
"reparametrization invariance of the string sigma-model action $$S_{\sigma}=\frac{-T}{2}\int d^2 \sigma \sqrt{-h}h^{\alpha \beta}\partial_{\alpha}X\cdot \partial_{\beta}X$$ allows us to choose two of the components of $h$, so that only one independent component remains. But this remaining component can be gauged away by using the invariance of the action under Weyl rescalings. As a result, the auxiliary field $h_{\alpha\beta}$ can be chosen as $$h_{\alpha\beta}=\eta_{\alpha\beta}=\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}."\tag{2.23}$$
I would really appreciate if someone could explain me how we can use reparametrization and Weyl invariance to get such a field $h_{\alpha \beta}$?
Recall that the action is under the resclaing $h_{\alpha\beta}\to e^{\phi(\sigma,\tau)}h_{\alpha\beta}$ and $\delta X^{\mu}=0$, and under reparametrization $\sigma^{\alpha}\to \sigma '^{\alpha}$.
