$[$Transformations$]$ A double transformation of a vector $c$ is a transformation Ac $($where A has components $a_{ij})$ followed by another transformation $B(Ac)($where $B$ has components $b_{ij}).$ Show that in general the double transformations $BAAB.$ An infinitesimal

transformation is a transformation I $+$ E is one that produces a new vector "nearly" equal to the old one: $I+E$ where $E$ is a tensor of infinitesimal elements. Show that $BA$~~$AB$ when A and $B$ are infinitesimal transformations.