Question: Similisât matrix of 2 squares

How to find the similarity matrix that applies A in N, B in P, C in C and B in M;
 

restart;  
with(geometry):  
with(plots):  
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':
#Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc
;

with(LinearAlgebra):
point(A, 0, 1);
point(B, 1, 1);
point(C, 1, 0);
point(E, 0, 0);
square(Sq, [A, B, C, E]);
Phi := (1 + sqrt(5))/2;
point(N, (2 - Phi)/(Phi - 1), 1);
line(BE, [B, E]);
MakeSquare(s1, [N, C, 'diagonal']);
point(M, (3 - sqrt(5))/(2*sqrt(5) - 2), (3 - sqrt(5))/(2*sqrt(5) - 2));
point(P, (1 + sqrt(5))/(2*sqrt(5) - 2), (3*sqrt(5) - 5)/(2*sqrt(5) - 2));
                               A

                               B

                               C

                               E

                               Sq

                             1   1  (1/2)
                      Phi := - + - 5     
                             2   2       

                               N

                               BE

                               s1

                               M

                               P

 display(draw([
A(color = black, symbol = solidcircle, symbolsize = 12),   
B(color = black, symbol = solidcircle, symbolsize = 12),   
C(color = black, symbol = solidcircle, symbolsize = 12),    
E(color = black, symbol = solidcircle, symbolsize = 12), 
N(color = black, symbol = solidcircle, symbolsize = 12 ),  
Sq(color=red),BE(color=green),  
s1(color = blue)]),   
textplot([[coordinates(A)[], "A"],   
[coordinates(B)[], "B"], 
[coordinates(E)[], "E"], 
[coordinates(N)[], "N"],
[coordinates(P)[], "P"],
[coordinates(M)[], "M"],   
[coordinates(C)[], "C"]], align = [above, right]), axes = none); Thank you.