A Determinantal Identity for the Permanent of a Rank 2 Matrix

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