  Multiparametric quantum semigroups $\mathrm{M}_{\hat{q}, \hat{p}}(n)$ are
generalization of the one-parameter general linear semigroups
$\mathrm{M}_q(n)$, where $\hat{q}=(q_{ij})$ and $\hat{p}=(p_{ij})$ are $2n^2$
parameters satisfying certain conditions. In this paper, we study the algebra
of multiparametric Manin matrices using the R-matrix method. The systematic
approach enables us to obtain several classical identities such as Muir
identities, Newton's identities, Capelli-type identities, Cauchy-Binet's
identity both for determinant and permanent as well as a rigorous proof of the
MacMahon master equation for the quantum algebra of multiparametric Manin
matrices. Some of the generalized identities are also generalized to
multiparameter $q$-Yangians.
