I have following block matrices:
$$M_1 = \left(\begin{array}{cc}A & B\\B' & D\end{array}\right)$$ and
$$M_2 = \left(\begin{array}{cc}A & -B\\-B' & D\end{array}\right)$$ I want to show that $\mathrm{eig}(M_1) = \mathrm{eig}(M_2)$. How can I prove that?