Prove that the transpose of an orthogonal matrix is an orthogonal matrix.
I think that the kroenecker delta needs to be used but not sure how to write it out.
What's the definition of "orthogonal matrix" you have? One of the equivalent ones is that a (real) square matrix $\displaystyle A$ is orthogonal iff $\displaystyle A^{-1}=A^t\Longleftrightarrow AA^t=I$ .
From here that your problem has an almost trivial proof.