Given two m x m matrix X and Y, where XY = YX. Let u be an eigenvector of X. Yu is an eigenvector of X. Suppose the eigenvalues of X are mutually different from each other and Y + 0. Show that Y and X have the same eigenvectors and the eigenvalues of Y are real.

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Q: Given two m ×m matrix X and Y , where XY = Y X. Suppose the eigenvalues of X are mutually different…

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