How to find rank of jacobian matrix?

My question is related to the symbolic math code which is below:

//Define Aa Matrix a11:=-(p1+p2); a12:=p2; a21:=p2; a22:=-p3; //Define Bb Matrix b11:=1; b21:=0;

Aa:=matrix([[a11, a12], [a21, a22]]);

Bb:=matrix([b11,b21]);

Cc:=transpose(matrix([1,0]));

G:=matrix([Cc*Bb,Cc*Aa*Bb,Cc*(Aa^2)*Bb,Cc*(Aa^3)*Bb]);

Gj:=linalg::jacobian([G], [p1, p2, p3])

linalg::rank(Gj)

the rank of Gj should be FULL.

But that is not what i get from the code.

how to implement "linalg::rank(Gj)" correctly ?

Calculation of rank of Gj becomes very difficult manually when Aa,Bb are function of many p1,p2.......

so my question is related to the implementation of "linalg::rank" of matrices such as Gj given above.

[Jan]

I have deleted my answer after the substantial editing of the question.