If A = [ij ~J and AB = BA, show that B = [~~J is also a diagonal matrix. B has the same

Chapter 6, Problem 34

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If A = [ij ~J and AB = BA, show that B = [~~J is also a diagonal matrix. B has the same eigen as A but different eigen . These diagonal matrices B form a two-dimensional subspace of matrix space. AB - BA = 0 gives four equations for the unknowns a, b, c, d-find the rank of the 4 by 4 matrix.

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