Let T be a linear operator on an inner product space V. Determine whether T is normal, self-adjoint, or neither. If possible, produce an orthonormal basis of eigenvectors of T for V and list the corresponding eigenvalues.

V= R^2 and T is defined by

T(a,b) = (2a-2b, -2a+5b)

Okay, so I already know that T is self-adjoint because T=T*

I just don't know how to do the second part for this particular problem.

Thanks so much!!!