Question

Is every Diagonalizable matrix invertible?​

Answer 1

After thinking about it some more, I realized that the answer is "Yes".

For example, consider the matrix

A=[1011].

It has two linearly independent columns, and is thus invertible.

At the same time, it has only one eigenvector:

v=[10].

Since it doesn't have two linearly independent eigenvectors, it is not diagonalizable.