Find the number of nonzero determinant of order 2 with elements 0 or 1 only.

Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of the set of all determinants with value -1 . Then

A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

A matrix is chosen at random from a set of all matrices of order 2 , with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non-zero will be :

Find the number of all possible matrices of order 3xx3 with each entry 0 or 1. How many of these are symmetric ?

A determinant of second order is made with the elements 0 and 1. Find the number of determinants with non-negative values.

Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9dot