# Every diagonalisable matrix has pairwise distinct eigenvalues

I need to prove whether or not every diagonalisable matrix has pairwise distinct eigenvalues.

My instinct is to think that the statement is true as for a matrix to be diagonalisable there has to exist a basis consisting of the eigenvectors of the matrix. However, I am unsure what is meant by 'pairwise distinct'.

• Look at identity matrix. It's diagonalisable and has only one eigenvalue. – user302982 Jan 12 '16 at 15:25
• The matrix $I$ is diagonalisable... but the eigenvalues aren't distinct. – user8469759 Jan 12 '16 at 15:25
• @sigmabe Oh, obviously!! Thank you :) – Nique Jan 12 '16 at 15:28