1. This work solves a problem whose simple special case occurs in a construction of a quantum unit ball of C (in the spirit of ). Within the framework of that theory, the automorphism group of the ball SU(n, 1) ⊂ SL(n + 1) is essential. The problem is that the Wess-Zumino differential calculus in quantum C  at a first glance seems to be only Uqslninvariant. In that particular case the lost Uqslm+n-symmetry can be easily detected. The main result of this work is in disclosing the hidden Uqslnsymmetry for bicovariant differential calculus in the quantum matrix space Mat(m,n). (Note that for n = 1 we have the case of a ball). The aurhors are grateful to V. Akulov and G. Maltsiniotis for a helpful discussion of the results.