Question

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.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Since |A| = 12

If A is a square matrix of order n

Then |Adj A| = `|"A"|^("n" - 1)`

∴ |Adj A| = `|"A"|^(3 - 1)`

= |A|²

= (12)²

= 144   ...[n = 3]