If the adjoint of a 3 × 3 matrix P is $\begin{bmatrix}1&4&4\\2&1&7\\1&1&3\end{bmatrix}$ the possible values of the determinant of P are
Answer & explanation
Correct answer: option 1
If A is an $n × n$ matrix, then $|adj\, A| = |A|^{n-1}$
$∴\begin{vmatrix}1&4&4\\2&1&7\\1&1&3\end{vmatrix}=|P|^2$
$⇒|P|^2=1(3-7)-4 (6-7)+4(2-1)=4$
$⇒|P|^2=± 2$