  Plancherel formula is one of the celebrated result of harmonic analysis on
semisimple Lie groups and their homogeneous spaces. The main goal of this work
is to find a q-analog of the Plancherel formula for spherical transform the
unit matrix ball. Here we present an explicit formula for the radial part of
the Plancherel measure. q-Jacobi polynomials as spherical functions naturally
arise on the way.
