Question

The value of a third order determinant is 5, then this value of the square of the determinant formed by its co-factors will be:

• A. 125
• B. 250
• C. 25
• D. 5

Answer 1

Answer: (A)

Note: Value of a determinant is the sum of the products of the elements of any row or column with the corresponding cofactor.
Given value of determinant = 5
Order of determinant = 3 $\times$ 3
Thus, let A be the value of determinant and n be the order. Then the square of the determinant formed by its cofactors
$=|A{|}^n=5^3=125$