Question:
Without expanding the determinant, prove that:
$\left|\begin{array}{ccc}1 & \mathrm{a} & \mathrm{bc} \\ 1 & \mathrm{~b} & \mathrm{ca} \\ 1 & \mathrm{c} & \mathrm{ab}\end{array}\right|=\left|\begin{array}{ccc}1 & \mathrm{a} & \mathrm{a}^{2} \\ 1 & \mathrm{~b} & \mathrm{~b}^{2} \\ 1 & \mathrm{c} & \mathrm{c}^{2}\end{array}\right|$
Solution:
