Invertible Continuous Linear Operator has Unique Inverse

Theorem
Let $\struct {X, \norm {\, \cdot \,} }$ be the normed vector space.

Let $\map {CL} X := \map {CL} {X, X}$ be a continuous linear transformation space.

Let $I \in \map {CL} X$ be the identity element.

Suppose $A \in \map {CL} X$ is invertible.

Then:


 * $\exists ! B \in \map {CL} X : A \circ B = B \circ A = I$