Exercise 2 (60 points) Analyze transpose algorithm Consider the problem to compute the transpose AT of an n x n matrix A. Consider the pseudocode to compute the transpose of an n x n matrix A transposeMatrix (A) for 1 to n = 1 to j - 1 // swap A[i][j] and 1: for i 2: 3: A[i] [j] buffer 4: A[i] [j] = A[j][i] A[j] [i] 5: buffer 6: All the questions in this exercise are related to the transposeMatrix(A) algorithm. The objective of this exercise is to explore whether the time complexity will change if we count different "actions" A) (16 points) Comparison Action In this case, we count the number of comparisons performed by the "for loops" (Lines 1 and 2). Answer the following questions to determine the total number of comparisons performed by the algorithm transposeMatrix(A). a. How many comparisons are performed by "for loop" in Line 1? b. Let us call t the number of comparisons performed by "for loop" in Line 2 for a given value of j. Fill in this table: 3 j n-1 c. Express the total number of comparisons performed by the "for loop" in Line 2 during the execution of transposeMatrix(A). d. Express the function fc(n) that represents the overall total number of comparisons performed by the "for loops" in Lines 1 and 2 during the execution of transposeMatrix(A). e. The function fe(n) grows like which function