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Maths-

General

Easy

Question

Let P be a non-singular matrix 1 + P + P² +….. + Pⁿ = O(O denotes the null matrix), then P^–1 is-

Pⁿ
– Pⁿ
– (1 + P + P² + ….+ Pⁿ)
None of these

The correct answer is: Pⁿ

Given 1 + P + P² + …… + Pⁿ = O
P^–1 + (P^–1 P) + (P^–1P)P + ….. + (P^–1 P)Pⁿ^–1 = O
$rightwards double arrow$ P^–1 + I + IP + ……..+ IPⁿ^–1 = O
$rightwards double arrow$ P^–1 = –(–Pⁿ) $rightwards double arrow$ P^–1 = Pⁿ

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