'Twas brillig, and the slithy toves did gyre and gimble in the wabe

Depends on the magnetization mechanism used - if they set off the ones in the store, they should have set off the library ones as well, since they often use the same system, however, in some cases the devices which test this use reversed polarity, so , it will not detect it if the library book would have set off the alarm in the library and will if it wouldn't have set off the alarm in the library.