This is a probem from "Matrix theory: basic results and techniques" page 147
Let $A$ be a matrix. If there is a Hermitian matrix $X$ such that $\left(\begin{array}{cc}I+X&A\\A^*&I-X\end{array}\right)$ is positive semidefinite. Then $|(Ay,y)|\le (y,y), \hbox{ for all $y$}.$
How to prove this?