Problem 1 (Matrix Powers). Let A be a m x n matrix. 1.1. What is a necessary and sufficient condition for the existence of the product A A? 1.2. Suppose A is an m x n matrix for which A A is defined, and that k N. Define recursively Ak when the base case is A = In. 1.3. Write an algorithm which takes as input values A and k and (i) Checks to see that A is a matrix and k a natural number (ii) Checks that A satisfies the condition explained in Problem 1.1. (iii) Recursively computes Ak if no errors occur in (i) or (ii). 1.4. Python uses the ** operator for powers by overloading a class method, --Pow__. Implement your algorithm as follows: class AlgoMatrix: def --pow__(self, k:int): " 'Returns self**k when k is a natural number.' # Implement your algorithm here. The coding portion of this problem should be completed at the bottom of the file ExamAlgoMatrix.py which is attached to the assignment