Verifying that a matrix is a rotation matrix

Hi!

How do you, properly, verify that a given matrix is a rotation matrix?

Consider the following matrix P:

where (for ) and else .

It's essentially an identity matrix with that familiar 2x2 rotation matrix setup sort of in the middle there. But mathematically, what conditions must I show are true to establish that this is a rotation matrix? I would think orthogonality is one of them?

Thank you in advance!:)

(sorry for the missing \cdots, I exceeded the limit of latex code:))