Without expanding the determinants, show that: i) | lll b+c & b c… - Vidyadip

Question

Without expanding the determinants, show that:
i) $\left|\begin{array}{lll}b+c & b c & b^2 c^2 \\ c+a & c a & c^2 a^2 \\ a+b & a b & a^2 b^2\end{array}\right|=0$
ii)$\left|\begin{array}{ccc}x a & y b & z c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{array}\right|$ =$\left|\begin{array}{ccc}x & y & z \\ a & b & c \\ b c & c a & a b\end{array}\right|$
iii) $\left|\begin{array}{lll}l & m & n \\ e & d & f \\ u & v & w\end{array}\right|=\left|\begin{array}{lll}n & f & w \\ l & e & u \\ m & d & v\end{array}\right|$
iv) $\left|\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right|=0$

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