Diagonalizability of a matrix A s.t. A^3 = A

[fortissimo]

Homework Statement

Well, I am constructing a proof for a statement, which builds upon the assumption that a matrix A satisfying A^3 = A is diagonalizable. According to http://crazyproject.wordpress.com/2011/12/08/any-matrix-a-such-that-a³-a-can-be-diagonalized/ this is true, however a reference is made to this "corollary 25 in D&F" (I assume it means Dummit's book in abstract algebra). Unfortunately I don't have access to this book, which makes it more difficult. Is it possible to find that theorem elsewhere, or will I have to work out the Jordan form for A (as can be done when A^2 = A)?

Homework Equations

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The Attempt at a Solution

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[morphism]

Hint: A matrix is diagonalizable iff its min poly splits into distinct linear factors.

 

[fortissimo]

Thank you, that would certainly prove the statement.