Row Reducing Quantum Matrices, the Quantum Determinant, and the Dieudonné Determinant Original Research Article

We prove that row reducing a quantum matrix yields another quantum matrix for the same parameterq. This means that the elements of the new matrix satisfy the same relations as those of the original quantum matrix ringMq(n). As a corollary, we can prove that the image of the quantum determinant in the abelianization of the total ring of quotients ofMq(n) is equal to the Dieudonné determinant of the quantum matrix. A similar result is proved for the multiparameter quantum determinant.