title: Hill Cipher using a 2 x 2 Key Matrix
body: <p>I'm new to cryptography and I cannot seem to get my head around this problem:
  The problem says that the Hill Cipher using the below 2 x 2 key matrix (K) was used to produce the ciphered text "KCFL". </p>
  
  <pre><code>K = (3   5)
      (2   3)
  </code></pre>
  
  <p>It then asks to use the Hill Cipher to show the calculations and the plain text when I decipher the same encrypted message "KCFL".</p>
  
  <p>I know with other matrices, e.g. for the determinant there is usually a formula, such as:</p>
  
  <pre><code>a x d - b x c
  </code></pre>
  
  <p>However, for the Hill Cipher I am completely lost.</p>
  
  <p>I have done the following:</p>
  
  <p>a) found the inverse of K:</p>
  
  <pre><code> K inverse =    (-3  5)
                  (2  -3)
  </code></pre>
  
  <p>b) Found "KFCL":</p>
  
  <pre><code>KFCL = (10  5)
         (2  11)
  </code></pre>
  
  <p>c) The next step (mod 26) confuses me. How do I decipher (using mod 26) and the Cipher Key to find the plain text?</p>
  
  <p>Any help is greatly appreciated.</p>
  
  <p>Many thanks.</p>