Linear algebra proof of $M(S \circ T) = M(S)M(T)$ I must provide proof of the following statement:
If $T,S \in L(V)$, then taking matrices with respect to $B$ (which is any basis of $V$), $M(S \circ T) = M(S)M(T)$

Make use of the fact that for any $v\in V$, the matrix of $T$ with respect to $B$ applied to $v$ expressed in base $B$ produces $T(v)$ expressed in base $B$.
