$1.$ Consider the directed graph shown in Figure $1.$

a$.$ What will be the page rank of the $3$ nodes? Explain with a clear argument why this is the case. Explain your calculations clearly.

b$.$ If the direction of the link from node C to node A is reversed, how $($and why$)$ do you expect the page rank of the nodes to change? You do not have to calculate the page ranks of the nodes, just explain how they may change and why.

Figure a$.$