Question

Evaluate $A=\left[\begin{array}{ccc}1& a& bc\\ 1& b& ca\\ 1& c& ab\end{array}\right]$

Answer 1

$A=\left[\begin{array}{ccc}1& a& bc\\ 1& b& ca\\ 1& c& ab\end{array}\right]$

$=1(a{b}^2-a{c}^2)-a(ab-ac)-bc(c-b)$

$={ab}^2-{ac}^2-a^{2}b+a^{2}c-{bc}^2+b^{2}c$

$=ab(b-a)+ac(a-c)+bc(b-c)$