If $B=\begin{bmatrix}1 & x & 0\\1& 3&3\\2 &0 &4\end{bmatrix}$ is the adjoint of matrix A of order $3×3$ and $|A|=4$ then the value of x is :

2

$B=\begin{pmatrix}1 & x & 0\\ 1 & 3 & 3\\ 2 & 0 & 4\end{pmatrix},\ B=\text{adj}(A),\ |A|=4$

$|\text{adj}(A)|=|A|^{2}=4^{2}=16$

$|B|=\begin{vmatrix}1 & x & 0\\ 1 & 3 & 3\\ 2 & 0 & 4\end{vmatrix}$

$=1\cdot\begin{vmatrix}3 & 3\\ 0 & 4\end{vmatrix}-x\cdot\begin{vmatrix}1 & 3\\ 2 & 4\end{vmatrix}$

$=1(12-0)-x(4-6)=12+2x$

$12+2x=16$

$2x=4$

$x=2$