J. Kalinowski
In the paper [4] similar problem and results concerning the preservers of
the determinant are presented. Let Φ : Mn(R) → Mn(R) be a linear operator.
In virtue [4, Theorem 3.1] we obtain that Φ is an operator preserving
the determinant if and only if there exist invertible matrices M, N ∈ Mn(R)
such that Φ(A) = MAN or Φ(A) = MAtN and det(MN) = 1, where At
denotes the transposition of the matrix A.
Acknowledgement. I would like to express my thanks to Professor
Mieczysław Kula for his valuable suggestions and remarks.