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Let A be an n n -th order square matrix with complex entries. Which of the following statements are true?

(a) A is always similar to a diagonal matrix.

(b) A

is always similar to an upper-triangular matrix.

(c) A is similar to a block diagonal matrix, with each diagonal block of size strictly less than n n , provided A

has at least 2

distinct eigenvalues B) is true as over complex characteristic polynomial of A is reducible in to linear factor A) is false in case of non zero nilpotent matrix..but I'm confused with option c.please help

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closed as off-topic by colormegone, Claude Leibovici, Leucippus, Milo Brandt, JonMark Perry Jun 5 '16 at 6:43

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