Linear Map Composition Associative Proof

Proof

1. Suppose we have $U\stackrel{R}{\to }V\stackrel{S}{\to }W\stackrel{T}{\to }X$ linear
2. We calculate $[(TS)R](u)=(TS)R(u)$
3. $=T(S(R(u)))$
4. Check other side, $[T(SR)]$
5. $=T(S(R(u)))$
6. As L.S = R.S, we have that they are equivalent