Coefficients affecting order & molecularity

[Janine Chan 2K]

Are the coefficients of the reactants correlated to the order/rate law of a reaction? Or is the rate law only dependent on the concentrations and rate constant given? I guess in other words, can we determine the order/rate law solely by looking at an equation and the coefficients?
For example, in 15.23c, we have the reaction 2 A -> B + C, but the problem states that the reaction is first order.

Or are coefficients only directly related to molecularity (where we saw that A+A--> products is bimolecular with a rate law or rate=k[A]²)?

[Lauren Seidl 1D]

The orders do not have to do with coefficients. If you look at problem 15.17, for example, the reactants all have different coefficients, but that does not affect their orders. You simply look at the concentrations for each when determining order. In 15.23c, however, you do need to use the coefficient in order to determine how much the concentration of A will decrease by.

[Alex Nechaev 1I]

I thought they were related at first as well, but the coefficients actually play no role in determining reaction order. For this, you look at concentrations and reaction rate.