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Question

Prove that :

1abc1bca1cab=1aa21bb21cc2

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Solution

Let LHS ==1 a bc1 b ca 1 c ab=1abca a2 abcb b2 bca c c2 abc Applying R1a R1, R2b R2 and R3c R3 and then dividing it by abc =abcabca a2 1b b2 1c c2 1 Taking out abc common from C3= -1 1 a2 a1 b2 b1 c2 c Interchanging C3 and C1 to get-ve value of original determinant=-1-11 a a21 b b21 c c2 Applying C2C3= 1 a a21 b b21 c c=RHS

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