
 a) Verify with numeric applications, 
    some basic properties and theorems IV. 
    
 b) The coefficients, integers or fractions, are randomly
    selected by the computer.

 c) The size of the matrices, are randomly selected by the 
    computer, but you can select the size if you want.


    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