Dynamic linking library

Suppose there are two executable elf . say A, B . And these two are
using  libctest.so.
When A is executed  libctest.so is loaded into RAM and linear address
is  correctly mapped.

If we execute program B after A ,  will library will be loaded again ?
else, how OS know that libctest is already loaded into physical page ?
(so it can  map linear address to it )

-Ratheesh