I am little bit confused about the idea of length contraction based on my textbook which did not elaborate this topic much.

lets say there are two guys named A and B. A is at rest and B is in motion relative to A with velocity v. A measures that a rod is $2$m long and tries to measure what its length would be observed with respect to B so he calculates the measurements and ends up having a result $2\gamma$m which is less than what he himself observed. By this example I tried to explain that the concept of length contraction is that the length calculated/measured by A which he thinks that B will be able to observe. I mean its like A asking himself "if I know its length is 2m, lets try and calculate how long will it be observed by B".

Is this understanding correct? Or am I thinking the opposite that is with respect to A, B will be able to measure the length of the rod to be $2/\gamma$m?