Let $A$, be a finite dimension algebra over a field K. $fA$ is a projective-injective right $A$-module, for some idempotent $f \in A$. So, $D(fA) \cong Ae$ for some idempotent $e \in A$.
I have seen in a place, that " $$fAf \cong End_{A^{op}}(fA) \cong End_A(D(fA))^{op} \cong End_A(Ae)^{op} \cong eAe$$
Via these isomorphisms, the right $eAe$-module $Ae$ becomes a right $fAf$-module."
I know that, $End_A(Ae)\cong eAe$ and $eAe$ is anti-isomorphic to $eAe^{op}$ as algebras, so who can tell me how to get the last isomorphism?