Question

A is a square matrix and I is a identity matrix of the same order. if A^3=0. the inverse of matrix (I-A) is

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

• Now if A is a square matrix then the type will be A mxm and I matrix will also be mxm since it is of same order.
• So the question is to find the inverse of I – A. Given A^3 = 0
•                            Now A^3 = 0
•                             Or – A^3 = 0
• Adding identity matrix I to both sides we get
•                              I – A^3 = I
• So we have the identity a^3 – b^3 = (a – b) (a^2 + ab + b^2)
•                        So we can write this as
•                               I^3 – A^3 = I
•                        (I – A) (I^2 - IA + A^2) = I
•                        (I – A) (I – A + A^2) = I------------1 (since identity matrix multiplied by any matrix will be that matrix)
•     Now we know that AA^-1 = I
•               Similarly (I – A) (I – A)^-1 = I ----------2
• By comparing 1 and 2 we  get (I – A)^-1 = I – A + A^2

Reference link will be

https://brainly.in/question/14926742?