Calculate Pagerank of three nodes
There is a formula for the PageRank which involves inverting an $n\times n$ matrix. When $n = 3$ this is not too hard. For inverting the matrix, use the formula given on Wikipedia, which is just a special case of the general formula involving the adjugate matrix.

That said, I see absolutely no reason why you would ever have to calculate PageRank by hand. That's what we have computers for. If you are given such an exercise in an exam, the matrix will probably have some very simple structure which will make it easier to handle by hand.