I'm trying to prove e(adsbygoogle = window.adsbygoogle || []).push({}); ^{A}e^{B}= e^{A + B}using the power series expansion e^{Xt}= [itex]\sum_{n=0}^{\infty}[/itex]X^{n}t^{n}/n!

and so

e^{A}e^{B}= [itex]\sum_{n=0}^{\infty}[/itex]A^{n}/n! [itex]\sum_{n=0}^{\infty}[/itex]B^{n}/n!

I think the binomial theorem is the way to go: (x + y)^{n}= [itex]\displaystyle \binom{n}{k}[/itex] x^{n - k}y^{k}= [itex]\displaystyle \binom{n}{k}[/itex] y^{n - k}x^{k}, ie. it's only true for AB = BA.

I'm really bad at manipulating series and matrices. Could I please get some hints?

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# Proof of commutative property in exponential matrices using power series

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