Poisson Bracket and commutators in quantum mechancs

Question

how did they reach the conclusion that quantization of the Poisson brackets

$ (A,B) $ was equal to the commutator $ \frac{1}{i\hbar}[A,B] $

in quantum mechanics?

so the quantum equations of motion were $ \frac{dA}{dt}= [A,B]\frac{1}{i\hbar} $