
 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.
 
    Try the examples in this order.

        Fraction      Integer

        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


