Suppose F is a field of characteristic not 2 with at least five elements.Let Mn(F) be the n × n full matrix algebra over F.The forms of linear maps preserving commutative {1}-inverses of matrices over Mn(F) are characterized.Using the conclusions of idempotent-preserving

it is proved that f is the nonzero linear maps from Mn(F) to Mn(F) preserving commutative {1}-inverses of matrices

if and only if there exists P∈GLn(F)

such that f(A) = εPAP-1

A∈Mn(F)

ε = ± 1∈F

or there exists P∈GLn(F)

such that f(A) = εPA...