a) Does inserting a node into a red-black tree, re-balancing, and then deleting it result in the original tree?

b) Does deleting a node with no children from a red-black tree, re-balancing, and then reinserting it with the same key always result in the original tree?

Please include specific example of a tree showing the original tree, the results of the re-balancing, and the final tree after deleting. Also include an explanation of how the algorithm proceeds to insert and delete nodes in the tree. Include information such as which node is the parent, grandparent, and uncle at each step, and which node is the argument for the left and right rotate steps. Refer to your specific trees in your explanation