Is Diagonalizability of Matrix A Proven by Eigenvalues in P^-1*A*P Columns?

[pyroknife]

The problem is attached. I just got some questions.
I attached a few problems. For these problems, to show that A is diagonalizable, it would be enough to show that the elements in each column of
P^-1*A*P corresponds to each eigenvalue?

 

[Mark44]

The problem is attached. I just got some questions.
I attached a few problems. For these problems, to show that A is diagonalizable, it would be enough to show that the elements in each column of
P^-1*A*P corresponds to each eigenvalue?

No attachment