Finding the Set of Permutable Matrices with Algebra

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To determine the set of permutable matrices with a given matrix A, one must find matrices X such that AX = XA. A key point is that for a matrix to be permutable, it typically requires that all rows and columns are consistent in structure. The discussion suggests that if matrix X has the same dimensions as matrix A, there could be infinitely many exchangeable matrices. The example provided illustrates a potential structure for such matrices. Understanding the properties of matrix multiplication is crucial for identifying these permutable matrices.
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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.
 
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Any thoughts on this?
 

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