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

                                 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)     

 