Q50 of 58 Page 77

State True or False for the statements

|A-1| ≠ |A|-1, where A is non-singular matrix.

False

Given A is non-singular matrix.


We know that AA-1 = I.


⇒|A||A-1| = 1


∴ |A-1| = 1/|A| = |A|-1


More from this chapter

All 58 →
48

State True or False for the statements

(A3)-1 = (A-1)3, where A is a square matrix and |A| ≠ 0.

 49

State True or False for the statements

(aA)-1 = (1/a) A-1, where a is any real number and A is a square matrix.

 51

State True or False for the statements

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

 52

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.