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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Determinants

If $A=\begin{bmatrix}\large\frac{1}{a}&a^2&bc\\\large\frac{1}{b}&b^2&ca\\\large\frac{1}{c}&c^2&ab\end{bmatrix}$ then $|A|$ is

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;-1&(D)\;abc\end{array}$

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1 Answer

$|A|=\large\frac{1}{abc}$$\begin{vmatrix}1 & a^3&abc\\1&b^3&abc\\1&c^3&abc\end{vmatrix}$
$\;\;\;\;=\large\frac{abc}{abc}$$\begin{vmatrix}1 & a^3&1\\1&b^3&1\\1&c^3&1\end{vmatrix}$
$\;\;\;\;=0$
Hence (A) is the correct answer.
answered Apr 22, 2014 by sreemathi.v
 

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