Eachindex efficiency on row-major arrays

I’m confused by these seemingly contradicting facts:

  1. From eachindex docstring:

    Create an iterable object for visiting each index of an AbstractArray A in an efficient manner

    (emphasize mine)

  2. A transposed view of a Matrix, which has a row-major layout, has eachindex yielding indexes in a column-major way:

julia> A = collect(reshape(1:6, 2, 3))
2×3 Matrix{Int64}:
 1  3  5
 2  4  6

julia> AA = transpose(A)
3×2 LinearAlgebra.Transpose{Int64, Matrix{Int64}}:
 1  2
 3  4
 5  6

julia> for i in eachindex(AA)
           print(AA[i], "  ")
       end
1  3  5  2  4  6

Is there a constraint that eachindex must follow column-major order? If so, where is it documented?

Seems that there should be an eachindex specific for LinearAlgebra.Transpose type, doesn’t it? Apparently there is no such specialization, all call the same function defined for AbstractArrays.

See What depends on AbstractArray Iteration Order?