111abca2-bcb2-cac2-ab = - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
0
B
1
C
abc
D
ab + bc + ca

Solution:

$|\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} - b c & b^{2} - c a & c^{2} - a b \end{matrix}| = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}| - |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ b c & c a & a b \end{matrix}| = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}| - \frac{1}{a b c} |\begin{matrix} a & b & c \\ a^{2} & b^{2} & c^{2} \\ a b c & a b c & a b c \end{matrix}| = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}| - \frac{a b c}{a b c} |\begin{matrix} a & b & c \\ a^{2} & b^{2} & c^{2} \\ 1 & 1 & 1 \end{matrix}| = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}| - |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}| = 0$

$|\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} - b c & b^{2} - c a & c^{2} - a b \end{matrix}| =$

Solution:

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