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If the adjoint of a $3\times 3$ matrix P is $\begin{bmatrix}1 &4&4\\2&1&7\\1&1&3\end{bmatrix}$ then the possible value(s) of the determinant of P is

$(a)\;\pm 2\qquad(b)\;-1\qquad(c)\;1\qquad(d)\;3$

1 Answer

We know for a third order matrix P.
$\mid Adj P\mid=\mid P^2\mid$
Where $\mid Adj P\mid=1(3-7)-4(6-7)+4(2-1)$
$\Rightarrow 4$
$\mid P^2\mid=4$
$\mid P\mid=\pm 2$
Hence (a) is the correct answer.
answered Nov 21, 2013 by sreemathi.v

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