Linear preservers of G-matrices on M2 ‎

Let Mn be the set of all n×n real matrices. A nonsingular matrix A ∈ Mn is called a G-matrix if there exist nonsingular diagonal matrices D1 and D2 such that A−T= D1AD2, where A−T denotes the transpose of the inverse of A. Let Gn be the set of all n×n G-matrices. A linear operator T : Mn → Mn is called a linear preserver of G-matrices if T(Gn) ⊆ Gn. The purpose of this paper is to find the structure of the linear operator preserving G-matrices on M2.