hi

You need to find the eigenvalues of the matrix, and find the corresponding eigenvectors. Do you know how to do this?

, since A is orthogonally diagonizable, P will be an orthogonal matrix, hence .

An easy way to find the eigenvalues of this matrix would be a cofactor expansion for example, or you could use the fact that it is block triangular.

Itīs quite a long process to describe if you have no idea whatsoever on how to find eigenvalues or eigenvectors, and I would in that case suggest you start there.