`*` and `UniformScaling`

I'm seeing some strange typing when multiplying StaticArrays and UniformScaling. Is all of this expected?

N = 2

typeof(rand(SMatrix{N,N}) * I)  # SMatrix{N, N}

typeof(rand(SMatrix{N,N}) * I(N))  # Matrix

typeof(rand(SVector{N}) * I)  # Matrix

typeof(I * rand(SVector{N}))  # SVector{N}

typeof(rand(SVector{N}) * I(1))  # Matrix

typeof(I(N) * rand(SVector{N}))  # SizedVector{N}

Should all these be outputs <: StaticArray?

If not, what is the rule for expected output type of these operations?

Reproduce the six Julia expressions involving StaticArrays and UniformScaling, recording each resulting type. Read the existing multiplication and type-promotion behavior, then establish the intended rule for these combinations; done means the expected outputs are agreed and the behavior or documentation is updated accordingly.