Question

if A is a non zero square matrix of order n with det (I+A)≠0 and A³=0,where l,o are unit and null matrices of order n×n respectively then (1+A)-¹=​

Answer 1

det(I+A)=0

A3=0   where 0 is null matrix, I is the identity matrix

A3+I=I [adding I on both sides]

(A+I)(A2−IA+I2)=I [by the formula of a3+b3]

(A+I)(A2−A+I)=I

(I+A)(I+A)−1=I [by the rule of inverse matrix]

hence (I+A)−1=(A2−A+I)

Ans: I−A+A2

Answer 2

Answer:

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