Quadratic algebras of type AIII (III)

This is the last in a series of three articles studying some quadratic algebras related to quantized matrix algebras. Here we determine the full set of so-called cyclic representations of the quantized matrix algebra Mq(3). These are irreducible representations in which all generators are invertible and the assumption on q is that it is a primitive m-th root of 1, with m 3.