Question

If A is non-singular matrix and (A + l)(A - l) = 0 then A + A^-1 = ______.

Options

• 2A

• 0

• l

• 3l

Answer 1

If A is non-singular matrix and (A + l)(A - l) = 0 then A + A^-1 = 2A.

Explanation:

We have, A is non-singular matrix

∴ |A| = 0

and (A + l)(A - l) = 0

⇒ A² - I² = 0

⇒ A² = I² = I

⇒ A·A = I

⇒ A^-1 = A

∴ A + A^-1 = A + A = 2A