Let A be a square matrix such that A2 - A + I = 0, then write A-1… - Vidyadip

Question

Let A be a square matrix such that A² - A + I = 0, then write A^-1 interms of A.

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Answer

A² - A + I = 0
Px-multiplying with A^-1,
(A^-1 A) - (A^-1 A) + A^-1I = 0
IA - I + A^-1 = 0
A^-1 = I - A
Hence, A^-1 = I - A

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