
 a) Verify with numeric applications, 
    some basic properties and theorems III. 
    
 b) This is also an example of the use of the fonctions, 
    I have write.

 c) See your textbook, or ask to your teacher, if you do
    not know how to do the operations.

      Three versions :

    1) The matrices are declared in main() :
    2) The matrices are declared in the functions :
    3) Work with Dev-C++4 and  DJGPP 2.03,
        with your compiler I don't know.
 
    Try the examples in this order.

                                 The properties of zero matrices :

         pmzaf.exe   pmzai.exe :       A + 0 =  0 + A
         pmzbf.exe   pmzbi.exe :       A - A =  0
         pmzcf.exe   pmzci.exe :       0 - A = -A
         pmzdf.exe   pmzdi.exe :       A * 0 =  0 * A  = 0

                                 The properties of the transpose : 

         trpaf.exe   trpai.exe : ( A**T )**T =  A
         trpbf.exe   trpbi.exe : ( A + B)**T =  A**T + B**T
         trpcf.exe   trpci.exe : ( A - B)**T =  A**T - B**T
         trpdf.exe   trpdi.exe : (kA    )**T = kA**T
         trpef.exe   trpei.exe : (AB    )**T =  B**T * A**T 

                                 The theorem of transpose :
       
       trpinvf.exe trpinvi.exe :   inv(A**T) = (inv(A))**T

                                 The theorem of inverse matrices :
 
        invabf.exe  invabi.exe :   inv(AB)   =  inv(B) * inv(A)     

 