Suppose F is a field of characteristic not 2 and $F;{ eq};Z_3$. Let $M_n(F)$ be the linear space of all $n{ imes}n$ matrices over F, and let ${Gamma}_n(F)$ be the subset of $M_n(F)$ consisting of all $n{ imes}n$ involutory matrices. We denote by ${Phi}_n(F)$ the set of all maps from $M_n(F)$ to itself satisfying A - ${lambda}B{in}{Gamma}_n(F)$ if and only if ${phi}(A)$ - ${lambda}{phi}(B){in}{Gamma}_n(F)$ for every A, $B{in}M_n(F)$ and ${lambda}{in}F$. It was showed that ${phi}{in}{Phi}_n(F)$ if and only if there exist an invertible matrix $P{in}M_n(F)$ and an involutory element ${varepsilon}$ such that either ${phi}(A)={varepsilon}PAP^{-1}$ for every $A{in}M_n(F)$ or ${phi}(A)={varepsilon}PA^{T}P^{-1}$ for every $A{in}M_n(F)$. As an application, the maps preserving inverses of matrces also are characterized.