Sure. Division also is, in exactly the same elementwise way as addition.
For those who typically do matrix calculations? Yes, I guess. For everyone else? I really doubt.
But the thing is - it does not avoid them! See my previous post for example: how should one (having experience with other languages, eg python or R) guess that even though a .+ b does the expected broadcasting all the way down, a .* b gives results of the same shape (i.e. no errors anywhere) but completely different content (in case of Array{Array{2}})? Note I’m not talking about language designer perspective, only from the user’s point of view.
And regarding division specifically - even you say “some kind of inverse” suggesting it is not obvious. Indeed, I cannot even find in the docs what it does for vectors! Docs say Right division operator: multiplication of x by the inverse of y on the right. Ok, do we have vector inverses? No: inv([1, 2]) says no method. However, [1, 2] / [1, 2] gives some result…
UPD: actually, thinking about this I even can see a possible solution to the confusion. If all those matrix operations are defined in LinAlg, then maybe just don’t import (using) it by default and require explicit action from the user? Then all the arithmetics on 1/2-d arrays will just fail instead of returning some (unexpected to those not doing matrices at this time) result.