kinetics - Do coefficients matter in rate law?

For reaction $\ce{2A→B}$ (elementary step), according to the rate law, rate $= k [A]^2$.

In some calculations, we use $k[A]^2$ as the production rate of B. Why isn't it ${1 \over 2} k[A]^2$?

In this case, is the consumption rate of A also $k[A]^2$? If so, why are they the same when in fact two molecules of A produce one molecule of B?

I'm really confused about this part. Can anyone explain why coefficient doesn't play a role in this calculation? Thanks!