How to prove the matrix used was Orthogonal?

The question is "Demonstrate that the matrix used above was Orhtogonal.

Heres the answer, but I dont understand where the answer came from. I read a few articles but don't understand them too well.

Where do the 1's come from and the 0's? It isn't .707 x .707 or .707 + .707 so what else could it be?

Any help is appreciated!