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Q.

If A is a non zero square matrix of order n with det(I+A)0 and  A3=0 , where I, O are unit and null matrices of order n × n respectively then (I+A)1= =

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a

I+A1

b

IA+A2

c

I+A

d

I+ A+A2

answer is A.

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Detailed Solution

  I3+A3=(I+A)(IA+A2)=(IA+A2)(I+A) 

    I3+0 =(I+A)(IA+A2)=(IA+A2)(I+A)

I =(I+A)(IA+A2)=(IA+A2)(I+A)                                  

(I+A)1=IA+A2   

 

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