# Math Help - Question : Determinants

1. ## Question : Determinants

Hi please anyone help me with this question, its a combination of Permutations&Combinations and Determinants.

Q. There is a 3X3 determinant in which each element is either 1 or 0. It is given that aij = aji . There are total seven 1s in this determinants. How many such Determinants are possible?

There are nine elements in a 3x3 matrix: three on the main diagonal, and three pairs of off-diagonal elements. The condition $a_{ij} = a_{ji}$ says that the two elements in each off-diagonal pair are equal. If seven of the elements are 1 then only two elements are 0. There are two ways in which that can happen. Either the two elements in one of the off-diagonal pairs are both 0, or two of the elements on the diagonal are 0. Count the number of ways in which each of these possibilities can occur.