Question: Diagonalization Of Matrices

A quick question to help with some Classical Mechanics homework. If the determinant of a matrix is zero does that mean that it cannot be diagonalized ? Please feel free to elaborate. I truly appreciate everyone's help on this site. In case your interested the text is "Classical Mechanics" 3rd ed. by Goldstein, Poole, and Safko. Chapter 4, specifically problem 4.8. Thanks, v/r,
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