Set X contains 3n elements and set Y contains 2n elements, and they have n elements in common. How many elements does (X - Y) × (Y-X) have?

Let A = {- 3, - 2, - 1, 0, 1, 2, 3} and B = {0, 1, 4, 9} How many elements does the subset of AB corresponding to the relation R = {(x, y) : |x| < y} have, where x $\in$ A and y $\in$ B?

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?