IIT-JEE 2012 · Paper 2 · Mathematics Q59

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MathematicsMultiple correct+4Question 59 of 60

If the adjoint of a $3\times3$ 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 (are)

−2

−1

Answer and worked solution

Official answer: A, D

Determinant of the adjoint. For a $3\times3$ matrix, $\det(\operatorname{adj}P)=(\det P)^2$ .
$\det\begin{bmatrix}1&4&4\\2&1&7\\1&1&3\end{bmatrix}=1(3-7)-4(6-7)+4(2-1)=4.$

So $(\det P)^2=4$ and $\det P=\pm2$ .

(A), (D)

Topics:Adjoint and inverse Determinants and properties

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IIT-JEE 2012 · Paper 2, Mathematics question 59