We consider the model of a transverse vector (e.g. magnetic) field with the most general form of the nonlinearity, known as the A model, passively advected by a strongly compressible turbulent flow, governed by the randomly stirred Navier-Stokes equation. The full stochastic problem is equivalent to a certain renormalizable field theoretic model with an infrared- attractive fixed point. Thus, the scaling behaviour for the large-scale, long-distance behaviour is established. However, the question whether the parameter A tends to a certain fixed-point value of the renormalization group equations or remains arbitrary, cannot be answered within the one-loop approximation of our study.