State True or False for the statements|adj. A| = |A|2, where A is a square matrix of order two.

Q54 of 58 Page 77

State True or False for the statements
|adj. A| = |A|², where A is a square matrix of order two.

False

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

Here n =2,

⇒ |adj A| = |A|^n-1 = |A|

Hence the statement is false.

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.

State True or False for the statements

, where a, b, c are in A.P.

State True or False for the statements

The determinant is equal to zero.

State True or False for the statements

If the determinant splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is 8.