36 minutes ago, ryt said:

Aren't we than arriving to the matrix in left-hand form or it's still in a right-hand?

Handness of matrix determined by signs before sin as shown before. But construction of matrix is implementation defined. Just for some application we have a sin and cos values from other sources then direct sin and cos computation from angle. From example from cross and dot produuctions of some vectors and so on.  So for it cases better work a construction by inversing sin sign on matrice intead of inversing angle that as result is same, and still work for version with direct sin/cos computations from angle.

Set of matrix build functions is a library implementation defined same as way to avoid a matrices/vectors of different handness from interoperation. On most cases it just used a 2 set of matrix construction functions one for LH other for LH and library user have to keep in mind what system used for each instance. Other way is to make separate clases for LH and RH vectors and matrices, and separate it in compile time, becouse mirror  transformation (that a just a recalculation of data in matrix) inverse handness. Its way require to make separate classes for matrices that content any possible kinds and combination of kinds of transformations for each handness and restrict a usage of user-defined kind of transformations that is not a combination of predefined in library kinds.