What if we're solving algebraic equation? Example, for the equation above, let's say the question is initially:
6÷2A=?

And through some other equation solved, we got A=(2+1), or A=3

We substitute A with 3 in the initial equation, the answer should be 1 right?

However, if we take it that 2A is the lazy way of writing 2*A, it would be, as you say, 9. My opinion is that without the multiplication sign, the number accompanying the parentheses is actually a coefficient, although multiplication is implied, it is of a higher order than written out multiplication and division sign? 😛

Another reason for why I think so (I may be wrong or miss some mathematic convention) is due to distributive law, i.e.
4+2 = 2(2+1)

6÷(4+2) = 6÷2(2+1) =/=6÷2*(2+1)

https://en.wikipedia.org/wiki/Distributive_property