If $P=\begin{bmatrix}1 & x & 3\\1 & 3 & 3\\2 & 4& 4\end{bmatrix}$ is the adjoint of 3×3 matrix A and |A| is 4, then x is equal to :

11

The correct answer is option (3) → 11

$\begin{vmatrix}1 & x & 3\\1 & 3 & 3\\2 & 4& 4\end{vmatrix}=4^2$

$C_2→C_2-2C_1,C_3→C_3-2C_1$

$\begin{vmatrix}1 & x-2 & 1\\1 & 1 & 1\\2 & 0& 0\end{vmatrix}=2(x-2-1)=4^2$

$⇒x-3=8$

$x=11$