Nice to see the forum back again. It has been down for weeks hasn't it?
A question says: "Cayley proved in 1946 that, if S is a skew-symmetric matrix, then I+S is non-singular and A=(I-S)(I+S)^-1 is orthogonal. Find A when S=(0 3, -3 0) and show that it is orthogonal."
The second row of S is -3 0. I don't know why I am not able to find A. I will probably manage the final part myself.