Math Help - normal, self-adjoint or neither...

I need to prove whether the following linear operator is normal, self-adjoint, or neither, and if possible, to find an orthonormal basis of eigenvectors of T for V and the corresponding eigenvalues
Let V = $\mathbb{R}^2$ be an inner product space, let T be defined by T(a,b) = (2a-2b,-2a + 5b)

No idea how to do this ,any help please? thanks

2. find the associated matrix respect to the standard basis for $\mathbb R^2.$

$T$ is normal if $T\cdot T^*=T^*\cdot T,$ self-adjoint if $T=T^*.$

find $T^*,$ in order to do that, you're gonna have to get the associated matrix, but since we're working on real numbers, $T^*$ is just $T^t.$

as for the eigenvalues and eigenvectors, that's a quite straightforward work, and i got no time no help ya there, so i hope someone's gonna provide help there.