Solution for this matrix equation?

Question

How to find the 2-by-2 complex matrix $H$ (if there is one) for which $$H\left[\begin{matrix} a & b \\ b^* & c\end{matrix}\right]H^\dagger=\left[\begin{matrix} a & be^{-i\lambda} \\ b^*e^{i\lambda} & c\end{matrix}\right]$$

Answer 1

Hint: $$ \begin{pmatrix}a & be^{-i\lambda} \\ b^*e^{i\lambda}&c\end{pmatrix}= \begin{pmatrix}e^{-i\lambda} &\\ &1\end{pmatrix} \begin{pmatrix}a & b\\b^* &c\end{pmatrix} \begin{pmatrix}e^{i\lambda} &\\ &1\end{pmatrix}. $$