Off topic:Id match and Matrix multiplication

Question

[akang]

I have two files. Row id in File1 matches the column id in file2 (starting from column6 )except the last 2 characters. File1 has 50 rows and File 2 has 56 columns. If the id matches I want to multiply the value in column3 of File1 to the entire column in File2. and in the final output print only Column2 and column7 onwards from file2. Any awk or R suggestions?

File1
P1  A   -0.468018   -3.49806    
P2  A   0.0903727   0.675471    
P3  C   0.441187    3.29752 
P4  C   0.240075    1.79437 


File2
ID1 ID2 ID3 ID4 ID5 ID6 P1_A P2_A P3_C........
0 A01 0 0 0 0 0 2 1 
0 A04 0 0 0 0 11 0 
0 E05 0 0 0 0 0 1 2 
0 G06 0 0 0 0 2 0 2 

Output
ID2  P1 P2 P3........
A01  0*-0.468018 2*0.0903727 ....
A04  1*-0.468018 1*0.0903727...
E05  0*-0.468018 1*0.0903727....
G06  2*-0.468018 0*0.0903727...