Property of unitary operator

Question

Let $\Psi(x, y, z)$ and $\Phi(x, y, z)$ be two complex functions in $L^2$ space, and $U$ be an unitary operator in the complex $L^2$ space.

Prove that:

$$\int_{-\infty}^{+\infty} (U\Psi)^*(U\Phi) d^3r = \int_{-\infty}^{+\infty} \Psi^* \Phi d^3 r$$