What happens on the cristae and in the matrix of mitchondria?

The mitochondria are where cellular respiration takes place so they are the energy factories of the cell.  The mitochondria produce energy for the cells in the form of ATP and produce chemical precursors for the manufacture of many compounds.  In the matrix, the most important process that occurs is the Krebs Cycle, also know as the Citric Acid Cycle.  The cycle converts carbohydrates into carbon dioxide and water through a complicated process.  The cycle produce NADH which allows for the production of ATP on the cristae.  ATP is the molecule which stores and provides energy for all cell processes.  The cristae are formed by the folding of the inner membrane that surrounds the matrix.  On the inner membrane ATP is created from a series of electron transfers from NADH.