The third Hankel determinant for inverse coefficients of starlike functions of order 1/2

The sharp bound for the third Hankel determinant for the coefficients of the inverse function of starlike function of order $1/2$ is obtained. In light of this, we can deduce that the functionals $|H_3(1)(f)|$ and $|H_3(1)(f^{-1})|$ exhibit invariance on the class $\mathcal{S}^*(1/2)$.