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

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

find the larget value of a third- order determinant whose elements are 0 or 1.

Minimum value of a second order determinant whose each is either 1 or 2 is equal to

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

Show that the set of all prime numbers is infinite.

Write the set of all integers whose cube is an even integer.

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 )

Show that the sum of first n even numbers is equal to (1+1/n) times the sum of first n odd numbers.