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If A is non-singular and $A^{2} - 5 A + 7 I = 0$ then $I =$

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17A−57A−1

17A+57A−1

15A+75A−1

15A−A−1

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detailed solution

Correct option is C

A2−5A+7I=0 By right multiplication with A-1AAA-1-5AA-1+7IA-1=0 A-5I+7A-1=0⇒ 7A−1 =5I−A ⇒ I=75 A−1+15A

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If A is non-singular and A2–5A+7I=0 then I=

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If A is non-singular and $A^{2} - 5 A + 7 I = 0$ then $I =$