If A is a square matrix such that (A - 2I) (A + I) = 0, then A-1 =

Question

If A is a square matrix such that (A - 2I) (A + I) = 0, then A-1 = (A) (A - I/2) (B) (A + I/2) (C) 2(A - I) (D) 2A + I

Tardigrade Admin · Accepted Answer

(A - 2I)(A +I) = 0 ⇒ AA - A - 2 I = 0 (∵ AI = A) ⇒ A ((A-I/2)) = I ∴ (A-I/2) = A-1

Q. If A is a square matrix such that (A - 2I) (A + I) = 0, then $A^{- 1}$ =