Determinant bundle of $(p,q)$ forms

Question

My actual question is much simpler but I would be interested to what happens in a generic case as well. Here's three cases which I want to know in general:

1. $X$ Kähler 3-fold, what are the determinant bundles of $Λ^{0,1}(X)$ and $Λ^{0,2}(X)$ in terms of the canonical bundle $K_X$?
2. $X$ Kähler 4-fold, what is the determinant bundles of $Λ^{0,2}(X)$ in terms of the canonical bundle $K_X$?
3. $X$ Kähler $n$-fold, what is the determinant bundles of $Λ^{p,q}(X)$ in terms of the canonical bundle $K_X$? (the generic case)