Find The eigen value of P Let P,M,N be n$\times$n matrices such that M and N are non singular.If
x is an eigenvector of P corresponding to eigen value $\lambda$,then
an eigenvector of N$^{-1}M$PM$^{-1}N$ corresponding to eigenvalue
$\lambda$is
(a) MN$^{-1}$x (b) M$^{-1}Nx$ (c) NM$^{-1}x$ (d) N$^{-1}Mx$
One more thing that worries me is P and N$^{-1}MPM^{-1}N$ having
same eigen value .What makes it necessary?
My Approach : The only thing i know is since M and N are non-singular
N$^{-1}M$ and M$^{-1}N$ they will have same set of eigenvalues.I
don't know if it has anything to do with question.

As already said $Px=\lambda x$.
$$N^{-1}MPM^{-1}N=K \rightarrow N^{-1}MP=KN^{-1}M \rightarrow N^{-1}MPx=K(N^{-1}Mx) \rightarrow \lambda (N^{-1}Mx)=K(N^{-1}Mx) $$ and so, $K$ has eigenvalue $\lambda$ and eigenvector $N^{-1}Mx$
