Finding the Set of Permutable Matrices with Algebra

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SUMMARY

The discussion focuses on identifying the set of permutable matrices in the context of algebra, specifically when a square matrix X is exchangeable with another matrix A, defined by the condition AX = XA. It is established that for a matrix to be permutable, all rows and columns must be identical, and both matrices must have the same dimensions. The user posits that there exists an infinite number of matrices exchangeable with matrix A, provided they share the same number of rows and columns.

PREREQUISITES
  • Understanding of square matrices and their properties
  • Knowledge of matrix multiplication and commutativity
  • Familiarity with the concept of exchangeable matrices
  • Basic algebraic principles related to matrices
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  • Explore the concept of matrix commutativity in depth
  • Learn about the implications of matrix dimensions on permutability
  • Investigate examples of specific matrices that are exchangeable
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Students studying algebra, particularly those focused on linear algebra and matrix theory, as well as educators seeking to clarify concepts related to permutable matrices.

esmeco
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I have this question as homework from my Algebra class:
A square matrix X is called exchangeable with A if AX=XA.Determine the set of permutable matrices with
matrix.jpg
.

My question is,how do I find that set?I know that a matrix to be permutable all rows and columns must be the same and that a square matrix is composed by the same number of rows and columns.
Thanks in advance for the help!:wink:
 
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An example of a matrix that could be exchangeable with A could be X=2 3 ?
4 5

I think there would be an infinite number of matrices exchangeable with the matrix A if the matrix has the same number of rows and columns as matrix A.
 
Last edited:
Any thoughts on this?
 

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