Question

If A is a matrix such that A^4 = I , then show that A^-1 = A^3

Answer 1

ANSWER

Given, A2=A


A2−A=0


⇒∣A2−A∣=0


⇒∣A(A−I)∣=0


⇒∣A∣∣A−I∣=0


⇒∣A∣=0or∣A−I∣=0


⇒∣A∣=0,or∣A∣=1

Answer 2

$Given, A2=A$

$A2−A=0$

$⇒∣A2−A∣=0$

$⇒∣A(A−I)∣=0$

$⇒∣A∣∣A−I∣=0$

$⇒∣A∣=0or∣A−I∣=0$

$⇒∣A∣=0,or∣A∣=1$

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