Question

If A is matrix of size n × n such that A² + A + 2I = 0, then

(A) A is non-singular

(B) A is symmetric

(C) |A| ≠ 0

(D) A^-1 = - 1/2(A + I)

Answer 1

Answer is (A), (C), (D)

A(A + l) = 2l. Now

|A(A + l)| = |-2l|

⇒ |A| |A + l| = (-2)ⁿ ≠ 0

⇒ |A| ≠ 0, A{-1/2(A + l)} = 1

⇒ A^-1 = - 1/2(A + l)