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

A determinant is chosen at random from the set of all determinant of order 2 with elements 0 or 1 only. Find the probability that the determinant chosen is nonzero.

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

If Aand B are two events than the value of the determinant choosen at random from all the determinants of order 2 with entries 0 or 1 only is positive or negative respectively. Then (a) P(A) ge P(B) (b) P(A) le P(B) (c) P(A)= P(B)=1/2 (d)None of these

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

Find the largest value of a third order determinant whose elements are 0 or -1.

Show that the value of a third order determinant whose all elements are 1 or -1 is an even number.

If the value of a third order determinant is 12, then find the value of the determinant formed by replacing each element by its co-factor

Consider the determinants Delta=|{:(2,-1,3),(1,1,1),(1,-1,1):}|,Delta'=|{:(2,0,-2),(-2,-1,1),(-4,1,3):}| STATEMENT-1 Delta'=Delta^2 . STATEMENT-2 : The determinant formed by the cofactors of the elements of a determinant of order 3 is equal in value to the square of the original determinant.

A matrix is chosen at random from the set of all 2 xx 2 matrices with elements 0 and 1 only. The probability that positive, is