
 a) Verify with numeric applications, 
    some basic properties and theorems IV. 
    
 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.


        idmaF.exe,    idmaI.exe   :  (A+B)**2    = A**2 + AB + BA + B**2
        idmbF.exe,    idmbI.exe   :  (A-B)**2    = A**2 - AB - BA + B**2 
        idmcF.exe,    idmcI.exe   :  (A-B) (A+B) = A**2 + AB - BA + B**2 
 
        idma2F.exe,   idma2I.exe  :  (A+B)**2    != A**2 + 2AB + B**2
        idmb2F.exe,   idmb2I.exe  :  (A-B)**2    != A**2 - 2AB + B**2 
        idmc2F.exe,   idmc2I.exe  :  (A-B) (A+B) != A**2 -       B**2 

         invaF.exe,    invaI.exe  :  inverse(inverse(A)) =         A
        invanF.exe,   invanI.exe  :  inverse(A**n)       = inverse(A)**n

         symaF.exe,    symaI.exe  :   A + Transpose(A) : Is Symmetric
         symbF.exe,    symbI.exe  :   A * Transpose(A) : Is Symmetric
         symcF.exe,    symcI.exe  :   A - Transpose(A) : Is Skew-Symmetric