  In this note we are dealing with a particular class of quadratic algebras --
the so-called quantum matrix algebras. The well-known examples are the algebras
of quantized functions on classical Lie groups (the RTT algebras). We consider
the problem of constructing some projectors on homogenous components of such
algebras, which are analogs of the usual symmetrizers. The main objective of
this note is to present a method, which hopefully enables one to construct
symmetrizers on all homogenous components of the RTT algebras. We illustrate
the construction by two low-dimensional examples. A way of extending this
method onto other quantum matrix algebras is also discussed.
