Find out if nxn matrix is diagonalisable based on det(XI-A)

1. The problem statement, all variables and given/known data

If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.



2. Relevant equations



3. The attempt at a solution

 

Re: diagonalisable?

The identity matrix has only one distinct solution, 1, but it is diagonalisable...

So how do you go about checking whether or not a matrix is diagonalisable or not?