Adjoint of Composition of Linear Transformations is Composition of Adjoints

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

Let $A \in B \left({K, L}\right), B \in B \left({H, K}\right)$ be bounded linear transformations.

Then $\left({AB}\right)^* = B^* A^*$, where $^*$ denotes adjoining.

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

Thus, by Existence and Uniqueness of Adjoint, $\left({AB}\right)^* = B^* A^*$.