Adjoint of Composition of Linear Transformations is Composition of Adjoints

Theorem
Let $H, K, L$ be Hilbert spaces.

Let $A \in \map B {K, L}, B \in \map B {H, K}$ be bounded linear transformations.

Then $\paren {A B}^* = B^* A^*$, where $^*$ denotes adjoining.

Proof
Let $h \in H, l \in L$. Then:

Thus, by Existence and Uniqueness of Adjoint:
 * $\paren {A B}^* = B^* A^*$