2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78463We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the relations describing the algebras of functions, differential and integral calculi. This paper presents the proofs of these results.LaTeX 2.09, 45 pagesQuantum AlgebraComplex VariablesOperator Algebras81R50 (Primary) 81Q99 (Secondary)Quantum matrix ball: differential and integral calculitext