Why Aren't AXB and BXA Equal in Matrix Multiplication?

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Homework Help Overview

The discussion revolves around the properties of matrix multiplication, specifically addressing the assertion that AXB is not equal to BXA. The original poster seeks to understand this relationship without specific variables provided.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the need for examples to illustrate the inequality of AXB and BXA, with some suggesting that finding a counterexample would suffice to demonstrate the claim. There is also a clarification regarding the nature of the proof required, emphasizing that a single counterexample is sufficient.

Discussion Status

The conversation is active, with participants offering guidance on how to approach the problem. There is an acknowledgment that understanding the concept is evolving, particularly for the original poster.

Contextual Notes

No specific variables or numerical examples have been provided, which may limit the exploration of the topic. The discussion also highlights the distinction between proving an identity invalid and demonstrating it through counterexamples.

jcsolis
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Homework Statement




Show that AXB is not equal to BXA

No variables given..just this equation


Homework Equations






The Attempt at a Solution



I don´t know how to start...the only thing I know so far is that AXB is equal to -BXA
 
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Have you tried any examples at all? After all, if you know that AxB = -BxA, shouldn't it be very easy to find a counterexample?
 
let me try
 
A little comment on semantics... when a question asks you to prove an identity is invalid; e.g. to show that AxB is not BxA, that means you just need to find one counterexample. In particular, the problem is not asking you to prove AxB and BxA are unequal for every possible A and B.
 
Thanks for the help...I didn´t understand why it´s not equal and now I get it
 

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