
 a) I have put the code of the functions into the h file,
    to simplify the work.
 
    To compile file.c :   gcc -o file file.c 

 b) Use only signed integer with these functions.
    Small numbers : -9 < x < 9.
 
    Try the examples in this order.
                                                                  
               Find, without calculate AB :
               ==========================

    The value of the coefficient AB(i,j) : 

       coefab01.c  : 
       coefab02.c  : 
       coefab03.c  : 
 
    The i column of AB : 

        colab01.c  :
        colab02.c  :
        colab03.c  :

    The i row of AB : 

        rowab01.c  :
        rowab02.c  :
        rowab03.c  :

               Verify with numeric applications :
               ================================


   The properties of matrix arithmetic :

        paritha.c  :        A + B = B + A 
        parithb.c  :  (A + B) + C = A + (B + C)
        parithc.c  :       (AB) C = A   (BC)
        parithd.c  :  A (B + C)   = AB + AC
        parithe.c       (B + C) A = BA + CA
        parithf.c  :  A (B - C)   = AB - AC
        parithg.c  :    (B - C) A = BA - CA
        parithh.c  :  a (B + C)   = aB + aC
        parithi.c  :  a (B - C)   = aB - aC
        parithj.c  :    (a + b) C = aC + bC 
        parithk.c  :    (a - b) C = aC - bC 
        parithl.c  :       a (bC) = (ab) C
        parithm.c  :       a (BC) = (aB) C = B (aC)  
 

   The properties of zero matrices :

        pmzeroa.c  :  A + 0 =  0 + A
        pmzerob.c  :  A - A =  0
        pmzeroc.c  :  0 - A = -A
        pmzerod.c  :  A * 0 =  0 * A  = 0


   The theorem of inverse matrices :  inv(AB) = inv(B) * inv(A) 

           tinv2.c : (2x2)   
           tinv3.c : (3x3)   
           tinv4.c : (4x4)   
           tinv5.c : (5x5)   


   The properties of the transpose :

         ptrposa.c : ( A**T )**T =  A
         ptrposb.c : ( A + B)**T =  A**T + B**T
         ptrposc.c : ( A - B)**T =  A**T - B**T
         ptrposd.c : (kA    )**T = kA**T
         ptrpose.c : (AB    )**T =  B**T * A**T


   The theorem of transpose :  inverse(A**T) =  (inverse(A))**T

         ttrpos2.c : (2x2)   
         ttrpos3.c : (3x3)   
         ttrpos4.c : (4x4)   
         ttrpos5.c : (5x5)   

