If any two rows (or columns) of a determinant are identical, the value of the determinant is zero.

Consider the following statements: (i) If any two rows or coluns of a determinant are identical, then the value of the determinatn 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?

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(5,20),(0,-1)]

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(1,-3,2),(4,-1,2),(3,5,2)]

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(0,2,6),(1,5,0),(3,7,1)]

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(1,a,bc),(1,b,ca),(1,c,ab)]

The rate-determining step is :

If the value of a third order determinant is 11, find the value of the square of the determinat formed by the cofactors.

How the age of fossils is determined

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 )