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

[russdot]

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

Thanks

 

[Ben Niehoff]

Think of how $e^{A}$ is defined.

 

[russdot]

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!