Background: Suppose $0 \to B \to E -q-> A \to 0$ is a short exact sequence of C*-algebras. Since B sits as an ideal of E, there is a natural *-homomorphism from E to the multiplier algebra of B (by the universal property of B) which extends the identity map on B. Composing this map with the quotient by B map, we obtain the Busby map: $A \to M(B)/B$
We say the extension is trivial if the Busby map $A \to M(B)/B$ lifts to a *-homomorphism $A \to M(B)$.
I am wondering why does this imply that there is a *-homomorphism section $s: A \to E$ such that $q \circ s= id_A$?