Thanks guys for the previous answer, Now suppose if I have a matrix e.g
$$M_1 = \begin{pmatrix} \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} & B \\ B' & D \end{pmatrix}$$ and $M_2$ as
$$M_2 = \begin{pmatrix} \begin{pmatrix} a_{11} & -a_{12} \\ -a_{21} & a_{22} \end{pmatrix} & B \\ B' & D \end{pmatrix}$$
How can i prove for this as eig($M_1$) = eig($M_2$), can this be proven?