Question

Statement 1: If ‘A’ is an invertible matrix, then (A²)^–1 = (A^–1)²

Statement 2: If ‘A’ is an invertible matrix, then |A^–1| = |A|^–1

Options

• Statement 1 is true and Statement 2 is false.

• Statement 2 is true and Statement 1 is false.

• Both the statements are true.

• Both the statements are false.

Answer 1

Both the statements are true.

Explanation:

For Statement 1:

If A is an invertible matrix.

∵ (Aⁿ)^–1 = (A^–1)ⁿ  for any integer n

For n = 2

(A²)^–1 = (A^–1)² 

It is true.

For statement 2:

|AA^–1| = |I|

|A| |A^–1| = 1

⇒ `|A^-1| = 1/|A|`

⇒ |A^–1| = |A|^–1

It is true.