Determine whether the given map ∅ is a homomorphism.

Let M_n and R be as in Exercise 12. Let ∅(A)= tr(A) for A ∈ M_n, where the trace tr(A) is the sum of the elements on the main diagonal of A, from the upper-left to the lower-right corner.

Data from Exercise 12

Let M_n be the additive group of all n x n matrices with real entries, and let R be the additive group of real numbers. Let ∅(A) = det(A), the determinant of A, for A ∈ M_n.