The relations between different linear R_aR_b transformations are described．Based on the reduced echelon matrix，an algorithm MR_ab is proposed．By using the stan-dard linear R_aR_b transformations，the equivalence of the output equation system of MR_ab to the image equation system of linear R_aR_b transformations is proved．After discussion about the relations between the algorithm MR_ab and ALT，the following conclusion is obtained：it is unnecessary for the finite automaton public key cryptosystem FAPKC3 to include an-other cheek process in the key generator to seive out a finite automaton of which a weak in-verse can be obtained by ALT．