If Aα=cos⁡αsin⁡α−sin⁡αcos⁡α, then AαAβ is equal to

We have AαAβ=cos⁡αsin⁡α−sin⁡αcos⁡αcos⁡βsin⁡β−sin⁡βcos⁡β=cos⁡αcos⁡β−sin⁡αsin⁡β−sin⁡αcos⁡β−cos⁡αsin⁡β                                                         cos⁡αsin⁡β+sin⁡αcos⁡β−sin⁡αsin⁡β+cos⁡αcos⁡β=cos⁡(α+β)sin⁡(α+β)−sin⁡(α+β)cos⁡(α+β)=Aα+β