Equivalence of the two definitions of multiplier algebra.

Question

1. $M(A)=\{(L,R)\in B(A)\times B(A):aL(b)=R(a)b\ \text{for all }a,b\in A \}$, where $B(A)$ are the bounded linear operators on $A$.

2. $M(A)=\{x\in A'': xA,Ax\subseteq A\}$, where $A''$ is the enveloping Von Neumann algebra of $A$.

It is obviouse that $M(A)$ defined in 1 contains that in 2. But I don't know how to show the two definitions are equivalent.