 The existence of a unique pseudoinverse implies the existence of a unique inverse, but the opposite is not true.For example, in the symmetric inverse semigroup, the empty transformation Ø does not have a unique pseudoinverse, because Ø = Ø"f"Ø for any transformation "f".The inverse of Ø is unique however, because only one "f" satisfies the additional constraint that "f" = "f"Ø"f", namely "f" = Ø.