Is every Jordan block diagonalisable?

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Is every Jordan block diagonalisable?

I need to also give a short justification. Can anyone lend a hand?

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if every Jordan block would be diagonalizable, then every matrix would be diagonalizable, and then nobody would care about Jordan blocks.

Pick the smallest possible non-trivial Jordan block and try to diagonalize it. Just a tiny amount of work would had solved the problem for you.