What are the values of x that satisfy the equation $$\left| {\matrix{ x & 0 & 2 \cr {2x} & 2 & 1 \cr 1 & 1 & 1 \cr } } \right| + \left| {\matrix{ {3x} & 0 & 2 \cr {{x^2}} & 2 & 1 \cr 0 & 1 & 1 \cr } } \right| = 0$$ ?

What is the value of the determinant $$\left| {\matrix{ {1!} & {2!} & {3!} \cr {2!} & {3!} & {4!} \cr {3!} & {4!} & {5!} \cr } } \right|$$ ?

If $\Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} $ 

and A, B, C, D, G are the cofactors of the elements a, b, c, d, g respectively, then what is $bB+cC-dD-gG$ equal to?

. Consider the following statements in respect of the determinant 

$ \Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix} $

I. Δ is positive if $k>0$.

II. Δ is negative if $k<0$.

III. Δ is zero if $k=0$.

How many of the statements given above are correct?