  We consider Yang-Baxter equations arising from its associative analog and
study corresponding exchange relations. They generate finite-dimensional
quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic
algebras. Then we proceed to a natural generalization of the Baxter-Belavin
quantum $R$-matrix to the case ${\rm Mat}(N,\mathbb C)^{\otimes 2}\otimes {\rm
Mat}(M,\mathbb C)^{\otimes 2}$. It can be viewed as symmetric form of ${\rm
GL}(NM)$ $R$-matrix in the sense that the Planck constant and the spectral
parameter enter (almost) symmetrically. Such type (symmetric) $R$-matrices are
also shown to satisfy the Yang-Baxter like quadratic and cubic equations.
