Question

Let P be a non-singular matrix 1 + P + P² +….. + Pⁿ = O

(O denotes the null matrix), then P^–1 is-

• A. Pⁿ
• B. – Pⁿ
• C. – (1 + P + P² + ….+ Pⁿ)
• D. None of these

Answer 1

Answer: (A)

Pⁿ

Answer 2

Given 1 + P + P² + …… + Pⁿ = O

P^–1 + (P^–1 P) + (P^–1P)P + ….. + (P^–1 P)P^n–1 = O

Ž P^–1 + I + IP + ……..+ IP^n–1 = O

Ž P^–1 = –(–Pⁿ) Ž P^–1 = Pⁿ