12.4 – Inverse of Matrices
       A matrix- based cryptography system can be used to encode a message.  By 
       using matrix multiplication in the encoding process, an individual letter can 
       be encoded as a different letter in different parts of the coded message.  
       These ciphers are difficult to decode since they require the use of the 
       inverse of the encoding matrix.  During World War II, analysts were able to 
       break German codes using sophisticated decoding techniques.
          Notation:
          In order to be inverses: 
          Only certain types of matrices have inverses.  Which ones?
                                                   1
            Example 1: Show that matrix B is the multiplicative inverse of matrix A.
                To find the inverse of a 2x2 matrix:
                                                               2
           Example 2: Find the inverse of 
                       To find the inverse of ANY square matrix:
                                                                                     3
                          Example 3: Find the inverse of 
                  Example 4: Find the inverse of 
                                                                                     4