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.

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

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

If each element of a 3xx3 matrix A is multiplied by 3 , then the determinant of the newly formed matrix is :

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 ?

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) )

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 each element of a row is expressed as sum of two elements then verify for a third order determinant that the determinant can be expressed as sum of two determinants.