Using property of invariance

Question

If a,b,c are non zero real numberw then we have to find the value of determinant .

I tried using property of invariace to make it easier to solve . But not able to do this . Can anybody help me in this .

Answer 1

Multiply $R_1$ by $a$, $R_2$ by $b$ and $R_3$ by $c$. Then we can take $abc$ common from both $C_1$ and $C_2$. And then add $R_1$ to $R_3$ and take out $ab+bc+ca$ common from $C_3$. Then we have $C_2$ and $C_3$ are identical. By using properties of determinants, our required value is thus $0$.