If any two rows (or columns) of a determinant are identical then the value of the determinants is 0.

Consider the following statements : (i) If any two rows or columns of a determinant are identical, then the value of the determinant is zero. (ii) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (iii) If any two rows ( or columns) of a determinant are interchanged , then the value of the determinant changes in sign. Which of these are correct ?

Consider the following statements : (a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero (b) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (c) If any two rows or columns of a determinant are interchanged, then the value of the determinant changes in sign. Which of these are correct ?

If any two rows (or columns) of a determinant are interchanged then the sign of a determinant changes.

Prove that if each element of a row (or a column) of a determinant is multiplied by k, then its value gets multiplied by k.

If each element of a row (or a column) of a determinant is multiplied by a constant k then its value gets multiplied by k.

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability (1)/(2) )