tudy
  cross products and when we get to the high dimensional version of
  $u$-substitution. Determinants are only defined for square
  matrices.</p>

  <div class="definition">
    The determinant of a $2\times 2$ matrix is the number

    <span class="marginpar">
      We use vertical bars next to a matrix to state we want the
      determinant, so $\det A = |A|$.
    </span>

    \begin{align*}\det \begin{bmatrix}
        a&amp;b\\c&amp;d\end{bmatrix} &amp;=
    \begin{vmatrix}
        a&amp;b\\c&amp;d
 