Check diagonalizability through the characteristic polynomial

Question

Basically what is given is the characteristic polynomial of A $$p(x)=(2-x)^2$$ and I am asked if the matrix A is diagonalizable. I have already realized that $x=2$ is a root (eigenvalue) with multiplicity 2 which implicates the matrix being diagonalizable if and only if the Eigenspace with respect to 2 has dimension 2 but I have no clue about how to find this matrix A and the eigenspace.

Answer 1

Guide:

You just have to exhibit two matrices, one of which it is diagonalizable and one of which it is not.

You might want to try matrix of this form. $$\begin{bmatrix} 2 & x \\ 0 & 2\end{bmatrix}$$