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Linear algebra - show that $ e^{a+b}=e^a e^b, If $a$ and $b$ are $n\times n$ matrices such that $ab = ba$ (that is, $a$ and $b$ commute), show that $$ e^{a+b}=e^a e^b$$ note that $a$ and $b$ do not have to be. A&e | watch full episodes of your favorite shows, Stream full episodes of a&e series, including 60 days in, leah remini, live pd, intervention, nightwatch, and more.. Prove e^(a+b)=e^a*e^b*e^-k/2 if [a,b]=k | physics forums, And using a power series again, i found (e^a)*(e^b) = (e^b)*(e^a) * e^-k, which is clearly very close to what i am trying to show. i keep staring at that neat partial derivative of coefficients trick, trying to see.

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