Does \(A e^{iA} = e^{iA} A\)?

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If A is an operator, is it correct/allowed to say:
Ae^{iA} = e^{iA}A

Thanks
 
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Think of how e^{A} is defined.
 
Ah yes, so since e^{A} is defined with a power series e^{A} = 1 + A + \frac{A^{2}}{2!} + \frac{A^{3}}{3!} + ... and A commutes with itself then A would commute with e^{A}
Thanks!
 
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