Consider the following statements:

Statement-l: If X is an nn matrix, then det(mX) = $m ^ n$ det(X), where m is a scalar.

Statement-II: If Y is a matrix obtained from X by multiplying any row or column by a scalar m, then det (Y) = m det (X).

Which one of the following is correct in respect of the above statements?

Consider the following statements about

the matrix $M=\left[\begin{matrix}71&23&48\\ 57&28&29\\ 65&17&48\end{matrix}\right]$ 

Statement-I: The inverse of M does not exist.

Statement-II: M is non-singular.

Which one of the following is correct in respect of the above statements?

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?