State True or False for the statements

If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.

True

Let A be the determinant.

∴ |A| = 12

We know that if A is a square matrix of order n, then |adj A| = |A|^n-1

For n = 3, |adj A| = |A|^3-1

= |A|²

= 12² = 144

Hence the above statement is true.