  We prove an identity relating the permanent of a rank $2$ matrix and the
determinants of its Hadamard powers. When viewed in the right way, the
resulting formula looks strikingly similar to an identity of Carlitz and
Levine, suggesting the possibility that these are actually special cases of
some more general identity (or class of identities) connecting permanents and
determinants. The proof combines some basic facts from the theory of symmetric
functions with an application of a famous theorem of Binet and Cauchy in linear
algebra.
