Determine whether the given map ∅ is a homomorphism.

Let GL(n, R) be the multiplicative group of invertible n x n matrices, and let R be the additive group of real numbers. Let ∅: G L(n, R) → R be given by ∅(A)= tr(A), where tr(A) is defined in Exercise 13.

Data from Exercise 13

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.