If the value of a third order determinant is 12 , then the value of the determinant formed by replacing each element by its cofactor will be 144.

$\left|\begin{array}{lll}x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c\end{array}\right|=0$, where $a, b$ and $c$ are in AP.

$|\operatorname{adj} A|=|A|^2$, where $A$ is a square matrix of order two.

The determinant $\left|\begin{array}{lll}\sin A & \cos A & \sin A+\cos B \\ \sin B & \cos A & \sin B+\cos B \\ \sin C & \cos A & \sin C+\cos B\end{array}\right|$ is equal to zero.

If the determinant $\left|\begin{array}{lll}x+a & p+u & l+f \\ y+b & q+v & m+g \\ z+c & r+w & n+h\end{array}\right|$ splits into exactly $k$ determinants of order 3, each element of which contains only one term, then the value of $k$ is 8 .