I get to a dead end with the 5th part

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Homework Help Overview

The discussion revolves around finding the inverse of a linear transformation represented by the equation A² - A = -I. Participants are exploring the steps necessary to isolate A⁻¹ and clarify their understanding of the problem's requirements.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods to manipulate the given equation, including multiplying by A⁻¹ and exploring the implications of different algebraic transformations. There is also a mention of the need to eliminate A from the equation, indicating some confusion about the process.

Discussion Status

The conversation includes attempts to clarify the steps involved in deriving A⁻¹ from the original equation. Some participants have offered guidance on specific algebraic manipulations, while others express uncertainty about the approach taken. Multiple interpretations of the problem are being explored.

Contextual Notes

There is a reference to previous responses in the thread, indicating that some participants may be revisiting earlier suggestions or solutions. The original poster expresses frustration at reaching a dead end, which may suggest a lack of clarity in the problem setup or requirements.

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I had already answered this. Please stop double posting.

You are given that A2- A= -I for linear transformation A and you are asked to find A-1. In your solution you multiply both sides by A-1 (as I had suggested before) and get A- I= -A-1. Then you do a lot of things that I don't understand.

Just multiply on both sides by -1 to get A-1= I- A. What more do you want?
 
ohhh that's the answer
i thought that we need toeliminate A totally
 
Actually, way back where you had A(A- I)=-I you could have written that as A(I-A)= I and said "Since I-A, multiplying A give the identity, I-A must be the inverse of A!"
 

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