KINDLY DO QUICK IS POSSIBLE I NEED URGENT I WILL UPVOTE YOU . IT IS CRYPTOGRAPHY QUESTION

Question 3 3 (a) Albert has written an algorithm for finding the inverse of a 2-by-2 matrix. (i) Give an estimate, in terms of N, of the size of the input of this algorithm when the entries of the matrix are taken from natural numbers smaller than NEN. (ii) For matrix entries as in (i), Albert's algorithm computes the inverse in N2 + N steps. Is this a polynomial time algorithm? Justify your answer. (iii) Does the problem of finding the inverse of a 2-by-2 matrix belong to the class P? Justify your answer (but you do not need to give a rigorous proof). [4] [5] p-1 (b) For any integer a coprime to a prime number p, prove that a'2 = +1 (mod p). [5] (c) In lectures, you have seen a method to compute za mod n with at most 2 log, a multiplications and reductions modulo n (I called it "the fast method). Illustrate this method by calculating 5100 (mod 37). Show your working. [8