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−A+A2

b

I+ A+A2

c

I+A–1

d

I+A

answer is A.

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Detailed Solution

I3+A3=(I+A)(I−A+A2) = (I−A+A2)(I+A)     I3+0 =(I+A)(I−A+A2) = (I−A+A2)(I+A) I =(I+A)(I−A+A2) = (I−A+A2)(I+A)                                  ⇒ (I+A)−1 = I−A+A2
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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= =