Which Matrices Satisfy AB=BA for A=[1 0; 1 1]?

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Homework Help Overview

The discussion revolves around finding matrices B that commute with a given matrix A, specifically A = [1 0; 1 1]. The problem is situated within the context of linear algebra and matrix operations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants suggest expressing matrix B in terms of its elements and exploring the resulting equations from the commutation relation AB = BA. There is a mention of using the inverse of A in the discussion, which raises questions about its relevance.

Discussion Status

The discussion is ongoing, with participants exploring different methods to express and manipulate the matrices involved. Some guidance has been offered regarding the setup of matrix B, but there is no explicit consensus on the best approach yet.

Contextual Notes

Participants are working under the constraints of the problem as posed, with no additional information provided about the properties of the matrices or specific methods to be used.

gunnar
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I would appreciate if someone could help me with this one.

Matrix A=[1 0 ; 1 1]
I need to find all matrices that satisfy: AB=BA
How can I find them?
PLease help :cry:
 
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Try writing
[tex]B=\left(\begin{array}{cc}a & b \\ c&d \end{array}\right)[/tex]

and check what the constraints on a,b,c and d are.
 
did that. And put A(inverse)* [a b;c d] = C*A(inverse)
 
What does the inverse have to do with everything...?

Daniel.
 
yea, just write out AB=BA using B=[a,b;c,d] and A=[1,0;1,1]
and multiply out both sides.
 

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