# GATE | GATE-CS-2014-(Set-3) | Question 20

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2021

Let A be a square matrix of size n x n. Consider the following program. What is the expected output?

 `C = 100``for` `i = 1 to n ``do``    ``for` `j = 1 to n ``do``    ``{``        ``Temp = A[i][j] + C``        ``A[i][j] = A[j][i]``        ``A[j][i] = Temp - C``    ``} ``for` `i = 1 to n ``do``    ``for` `j = 1 to n ``do``        ``Output(A[i][j]);`

(A) The matrix A itself
(B) Transpose of matrix A
(C) Adding 100 to the upper diagonal elements and subtracting 100 from diagonal elements of A
(D) None of the above

Answer: (A)

Explanation: If we take look at the inner statements of first loops, we can notice that the statements swap A[i][j] and A[j][i] for all i and j. Since the loop runs for all elements, every element A[l][m] would be swapped twice, once for i = l and j = m and then for i = m and j = l. Swapping twice means the matrix doesnâ€™t change.

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