Looking at the answer of this question:
Show that the arc length of a curve is invariant under rigid transformation.
I don't understand why if $T$ is linear then
$$(T\circ \gamma)'(t)=T\circ \gamma'(t)$$
I will appreciate any comment to help me to understand
This is an application of the chain rule together with the fact that for any linear transformation $T,\ T'(x)=T:$
$(T\circ \gamma)'(t)=T'(\gamma (t))(\gamma'(t))=T(\gamma '(t))=T\circ \gamma'(t).$