As the title, let $(V,\langle,\rangle)$ be a complex inner product space and assume $S_1=(u_1,\ldots,u_n)$, $S_2=(v_1,\ldots,v_n)$ are orthonormal bases of $V$. Prove that the change of basis matrix $M_ IV(S_2,S_1)$ is a unitary matrix.
(There is a hint that let $S$ be the operator s.t. $S(u_i)=v_i$ and prove this is a unitary operator.)