Determinant preserving maps on matrix algebras Original Research Article

Let Mn be the algebra of all n×n complex matrices. If φ:Mn→Mn is a surjective mapping satisfying det(A+λB)=det(φ(A)+λφ(B)), A,Bset membership, variantMn, image , then either φ is of the form φ(A)=MAN, Aset membership, variantMn, or φ is of the form φ(A)=MAtN, Aset membership, variantMn, where M,Nset membership, variantMn are nonsingular matrices with det(MN)=1.