title: why is the time complexity of square matrix multiplication defined as O(n^3)?
body: <p>I have come across this in multiple sources (online and books) - Running time of square matrix multiplication is O(n^3) for matrices of size nXn. (example - <a href="https://stackoverflow.com/questions/8546756/matrix-multiplication-algorithm-time-complexity">matrix multiplication algorithm time complexity</a>)</p>
  
  <p>This statement would indicate that the upper bound on running time of this multiplication process is C.n^3 where C is some constant and n>n0 where n0 is some input beyond which this upper bound holds true. (<a href="http://en.wikipedia.org/wiki/Big_O_notation" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Big_O_notation</a> and <a href="https://stackoverflow.com/questions/471199/what-is-the-difference-between-n-and-on">What is the difference between Θ(n) and O(n)?</a>)
  Problem is, i cannot seem to derive the values of constants C and n0.</p>
  
  <p>My questions - </p>
  
  <ol>
  <li><p>Can someone provide a mathematical proof for the statement 'big Oh of square matrix multiplication is O(n^3)' ?</p></li>
  <li><p>what are the values of C and n0 ?</p></li>
  </ol>