Finding the Set of Permutable Matrices with Algebra

[esmeco]

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

.

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!

 

[esmeco]

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.

 

[esmeco]

Any thoughts on this?