  We propose and prove a set of identities for ${\rm GL}_M$ elliptic $R$-matrix
(in the fundamental representation). In the scalar case ($M=1$) these are
elliptic function identities derived by S.N.M. Ruijsenaars as necessary and
sufficient conditions for his kernel identity underlying construction of
integral solutions to quantum spinless Ruijsenaars-Schneider model. In this
respect the result of the present paper can be considered as the first step
towards constructing solutions of quantum eigenvalue problem for the
anisotropic spin Ruijsenaars model.
