Maps preserving idempotence on spaces of 2x2 symmetric matrices

Suppose F is an arbitrary field. Let S-2(F) be the space of all 2 x 2 symmetric matrices. A map Phi: S-2(F) -> S-2(F) is said to preserve idempotent relation if A -lambda B is idempotent if and only if Phi(A) -lambda Phi(B) is idempotent for any A, B is an element of S-2(F) and lambda is an element of F. We characterize the maps preserving idempotent relation on S-2(F) when the characteristic of F is 2.