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We consider the irreducible representations each of dimension 2 of thenecklace braid group $\mathcal{NB}_n$ ($n=2,3,4$). We then consider the tensorproduct of the representations of $\mathcal{NB}_n$ ($n=2,3,4$) and determinenecessary and sufficient condition under which the constructed representationsare irreducible. Finally, we determine conditions under which the irreduciblerepresentations of $\mathcal{NB}_n$ ($n=2,3,4$) of degree 2 are unitaryrelative to a hermitian positive definite matrix

Representations of the necklace braid group {NB}}_n of dimension (n=2,3,4)