  Let A and B be matrices of M_n(C). We show that if exp(A)^k
exp(B)^l=exp(kA+lB) for all integers k and l, then AB=BA. We also show that if
exp(A)^k exp(B)=exp(B)exp(A)^k=exp(kA+B)$ for every positive integer k, then
the pair (A,B) has property L of Motzkin and Taussky. As a consequence, if G is
a subgroup of (M_n(C),+) and M -> exp(M) is a homomorphism from G to
(GL_n(C),x), then G consists of commuting matrices. If S is a subsemigroup of
(M_n(C),+) and M -> exp(M) is a homomorphism from S to (GL_n(C),x), then the
linear subspace Span(S) of M_n(C) has property L of Motzkin and Taussky.
