Question

For a square matrix A, (3A)^–1 = ______. 

Options

• 3A^–1

• 9A^–1

• `1/3`A^–1

• `1/9`A^–1

Answer 1

For a square matrix A, (3A)^–1 = `bbunderline(1/3A^(–1))`. 

Explanation:

3A^–1 

(KA)^–1 = `1/k` A^–1 

`(3A) (1/3A^(–1))=(3*1/3) (A*A)`

= 1 ⋅ I 

= I