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 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If each element of a row is expressed as sum of two elements then verify for a third order determinant that the determinant can be expressed as sum of two determinants.

The value of the determinant of a matrix A of order 3 times 3 is 4. Find the value of |5A|.

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) )

The houses of a row are numbered consectively from 1 to 49. show that there is a value of x such that the sum of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

A determinant is chosen at random from a set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

A determinant si chosen at random from the set of all determinats of order 2 with elements - and 1 only . The probability that the value of the determinant chosen is positive is :