In the frame of reference of ruler A, the ruler B will be shorter. In the frame of reference of ruler B, then ruler A will be shorter.
Thank you for your answers. It is clearer to me now, even though I still don't understand it.
I have this one more related problem that concerns length contraction.
So, a ruler of length 100 cm moves at a relativistic speed and passes near another, stationary, 100 cm ruler.
My question is: Will the observers on both rulers see that both rulers have identical length? That is to say, will there be no length contraction?
You might be interested in the ladder paradox for a conceptual application of this phenomenon.
That's a very good question indeed. I am really not sure, but I would take the point of view that it is "real" (whatever that means), rather than just an illusion, because length contraction is analogous to time dilation which is clearly very "real". Moreover, the ladder paradox above suggests that length contraction IS real and not a mere illusion.
I mean, is the length contraction just an illusion caused by light lag?