If |a1b1c1a2b2c2a3b3c3|=5 then the value of |b2c3−b3c2a3c2−a2c3a2b3−a3b2b3c1−b1c3a1c3−a3c1a3b1−a1b3b1c2−b2c1a2c1−a1c2a1b2−a2b1| is

LetA=[a1b1c1a2b2c2a3b3c3]Given that |A|=5 LHS=|cofactor matrix of A| =|AdJA|=|A|3−1=52=25

If |a1b1c1a2b2c2a3b3c3|=5 then the value of |b2c3−b3c2a3c2−a2c3a2b3−a3b2b3c1−b1c3a1c3−a3c1a3b1−a1b3b1c2−b2c1a2c1−a1c2a1b2−a2b1| is

LetA=[a1b1c1a2b2c2a3b3c3]Given that |A|=5 LHS=|cofactor matrix of A| =|AdJA|=|A|3−1=52=25

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If $| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} | = 5$ then the value of $| \begin{matrix} b_{2} c_{3} - b_{3} c_{2} & a_{3} c_{2} - a_{2} c_{3} & a_{2} b_{3} - a_{3} b_{2} \\ b_{3} c_{1} - b_{1} c_{3} & a_{1} c_{3} - a_{3} c_{1} & a_{3} b_{1} - a_{1} b_{3} \\ b_{1} c_{2} - b_{2} c_{1} & a_{2} c_{1} - a_{1} c_{2} & a_{1} b_{2} - a_{2} b_{1} \end{matrix} |$ is

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Detailed Solution

$L e t A = [\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}]$
Given that $| A | = 5$
$L H S = | c o f a c t o r matrix of A | \begin{array}{l} = | A d J A | \\ = {| A |}^{3 - 1} \\ = 5^{2} = 25 \end{array}$