Let K be a topological field. On introducing the vector-space topology on the n × n matrices over K, it becomes clear that the determinant map φ enjoys the following properties:(A) φ is a continuous surjective homomorphism from GL_n(K) to K*,(B) φ(μa) = μ_n φ(a) for each non-zero φ in K, and all a in GL_n(K).