Decide if the following statements are TRUE or FALSE. Write a proof for the true ones and provide a counter-example for the

Question

Decide if the following statements are TRUE or FALSE. Write a proof for the true ones and provide a counter-example for the rest.
Every linear operator T: Rⁿ → Rⁿ can be written as T = D + N, where D is diagonalizable, N is nilpotent and DN = ND.

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