Question

Evaluate $\left|\begin{array}{ccc}a& b& c\\ -1& 1& -1\\ 1& -1& 1\end{array}\right|$.

Answer 1

$A=\left|\begin{array}{ccc}a& b& c\\ -1& 1& -1\\ 1& -1& 1\end{array}\right|$

$A=a(1-1)-b(-1+1)+c(1-1)$

$A=a\times 0-b\times 0+c\times 0=0$