[math-fun] exp(A)exp(B) = exp(A+B) = exp(B)exp(A)?

From: Dan Asimov <dasimov@earthlink.net> It's well known and easy to prove that if NxN matrices A and B commute, then (*) exp(A)exp(B) = exp(A+B) = exp(B)exp(A) But ... can happen if A,B do not commute... I think such examples of complex matrices are easier to come by than of real ones, so I'm particularly interested in the case where A and B are real.

-- 1. I point out, that any complex A,B example using nXn matrices, can immediately be converted to equivalent 2nX2n real matrices. 2. Initially I would suggest seeking upper triangular A,B.