Inverse of hermitian operator

Question

If $A$ is hermitian operator on finite-dimensional inner-product vector space $V$, than prove $A^{-1}$ is also hermitian operator.

( Hermitian operator $A$ is operator such that $A=A^{*}$ )

Answer 1

Hint: Show that $(A^*)^{-1} = (A^{-1})^*$. In order to show that this is the case, it suffices to show that $$ A^*(A^{-1})^* = I $$