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

± 2 ± 1 ± 3 ± 4

± 2

If A is an $n × n$ matrix, then $|adj\, A| = |A|^{n-1}$ $∴\begin{vmatrix}1&4&4\\2&1&7\\1&1&3\end{vmatrix}=|P|^2$ $⇒|P|^2=1(3-7)-4 (6-7)+4(2-1)=4$ $⇒|P|^2=± 2$