Matrix Similarity Proof - need someone to check if it's correct

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    Matrix Proof
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Homework Help Overview

The discussion revolves around the concept of matrix similarity, specifically examining the relationship between two matrices A and B, where A is defined as the identity matrix. The original poster seeks validation of their reasoning regarding when B can be considered similar to A.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish that if B is similar to A, then A must also be similar to B, using the property of similarity. They question whether their reasoning is circular. Other participants engage by discussing the identity matrix's properties and the necessity of demonstrating the bidirectional nature of similarity.

Discussion Status

The discussion is ongoing, with participants providing supportive comments and raising questions about the necessity of proving certain properties of similarity. There is an exploration of the implications of the identity matrix in this context.

Contextual Notes

Participants note the lack of answers in the textbook and the implications of the identity matrix in the discussion. There is an emphasis on clarity regarding the properties of matrix similarity.

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Homework Statement


My textbook has no answers so I was wondering if someone could let me know if I'm right.

The question: A and B are m x n matrices.
Let A = I. Find when B = A.

Homework Equations


The Attempt at a Solution


What I did seems too easy:

If B ~ A, then A ~ B (this is just a property of similarity)

Since A = I, we can sub in for A

So B = A

Did I just argue myself in circles?
 
Last edited:
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That's fine. You can take the 'I' out because IP=P. 'I' is the identity matrix.
 
Great, thank you! Do you think it's necessary to show that if A ~ B, B ~ A?
 
jumbogala said:
Great, thank you! Do you think it's necessary to show that if A ~ B, B ~ A?

If you're not clear on why it's true, you should probably show it. It's easy enough.
 

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