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If A is a square matrix such that (A−2I)(A+I)=0 ,then A−1=

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a

A−I2

b

A+I2

c

2(A−I)

d

2A+I

answer is A.

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Detailed Solution

(A−2I)(A+I)=0 AA−2AI+AI−2I=0 (∵ AI=A)AA-AI=2I⇒A(A−I2)=I ∵A−I2=A−1

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