Is Every Statement About Matrix Squares True?

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Homework Help Overview

The discussion revolves around properties of square matrices, specifically focusing on statements regarding matrix squares and their implications. The subject area includes linear algebra and matrix theory.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are examining the truth of specific statements about square matrices, questioning their validity based on examples and counterexamples. There is an exploration of intuitive reasoning regarding the statements presented.

Discussion Status

Participants are actively engaging with the statements, with some providing intuitive responses while others seek to verify or challenge these intuitions through examples. There is an indication of productive questioning, particularly regarding the search for counterexamples.

Contextual Notes

Some participants express uncertainty about the statements and are encouraged to find counterexamples to support their claims. The discussion is framed within the context of verifying mathematical assertions without providing definitive answers.

tysonk
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Can someone verify these for me and explain?
True/False
No square matrix with real entries can obey A^2 = -I
The only 2X2 matrix that obeys A^2 = 0 is A=0
The only 2X2 matrices that obey A^2=A are A=0 and A=I

Much appreciated.
 
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Do you think they are true or false?
 
Last edited:
Intuitively,
-false
-false
-true
 
What about A^2 when A={{1,0},{0,0}}?
You can show a statement is false with one example.
Can you find counter examples for the first 2?
 

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