title: What is the concatenation of this language with itself?
body: <p>Given the following language: </p>
  
  <blockquote>
    <p><code>L<sub>1</sub> = { (ab)<sup>n</sup> | n &ge; 0 }</code></p>
  </blockquote>
  
  <p>That is, <code>L<sub>1</sub> = { &epsilon; ab, abab, ababab, abababab, ... }</code></p>
  
  <p>The question is to find what language <code>L<sub>1</sub><sup>2</sup></code> is.</p>
  
  <p>My guess is that it's equal to <code>{ (ab)<sup>2n</sup> | n &ge; 0 }</code>. Is that correct? If so, how do I prove it? If not, why not?</p>
  
  <p>Thanks!</p>