</div>=6$ and $

      <div class="vmatrix">
        {1}&amp;{3}\\{2}&amp;0
      </div>=-6$
    </div>\caption{The determinant gives both area and direction. A
    counter clockwise rotation from column 1 to column 2 gives a
    positive determinant.\label{detfig}}
  </div>% }}
  </div>

<p>For a 3 by 3 matrix, the columns give the edges of a three dimensional parallelepiped and the determinant produces the volume of this object. The sign of the determinant is related to orientation. If you can use your ri