Argac, N.Eroglu, M. P.Lee, T. -K.Lin, J. -H.2020-12-012020-12-0120200308-10871563-5139https://doi.org/10.1080/03081087.2019.1575331https://hdl.handle.net/11454/62584Motivated by [1, 2], the goal of the paper is to study certain identities with inverses on matrix rings. Given D a division ring, we characterize additive maps f,g:D -> D satisfying the identity f(x)x-1+xg(x-1)=0 for all invertible x is an element of D. Let R be a matrix ring over a division ring of characteristic not 2. We also characterize additive maps f,g:R -> R satisfying the identity f(x)x-1+xg(x-1)=0 for all invertible x is an element of R. Precisely, there exist an element q is an element of R and a derivation d of R such that f(x)=xq+d(x) and g(x)=-qx+d(x) for all x is an element of R. This affirmatively answers the question below Theorem 4 in [1] due to L. Catalano.en10.1080/03081087.2019.1575331info:eu-repo/semantics/closedAccessDivision ringderivationinversematrix ringfunctional identityArticle683635651WOS:000587891600014Q1