In C, to swap two rows of a matrix mat of size n x n, which of the following statements is correct?

Ben is studying matrices and wants to write a program that swaps two rows of a matrix (N, M), the program takes an input matrix, swaps the specified rows, and then displays the modified matrix.Assist him with the program.Input format :The first line consists of two space-separated integers N and M, representing the number of rows and columns in the matrix.The next N lines contain M space-separated integers each, representing the elements of the matrix.The last line consists of two space-separated integers r1 and r2, representing the row numbers to be interchanged.Output format :If the input row numbers r1 or r2 are invalid (less than 1 or greater than the number of rows), the output prints "Invalid row numbers".Otherwise, the modified matrix is printed after swapping the specified rows.

A mirror image of a 2D array of m*n, elements of the first and the last columns are interchanged.Second and one before the last interchanged and so on. The middle column remains fixed. Onlythe columns of a mirror image are interchanged row remains unaffected.Write a C program to do the following.a) Declare a 2D integer array called matrix of size 5 by 5.b) Input set of positive numbers and store in the array.Enter 1,1 :………….Enter 1,2 :………….Enter 1,3 :………….c) Display the array in the tabular format.5 4 3 7 68 1 2 9 27 3 4 1 03 6 9 2 31 4 9 3 0d) Find the mirror image of the matrix without using an additional array.e) Display the new array in the tabular format.6 7 3 4 52 9 2 1 80 1 4 3 73 2 9 6 30 3 9 4 1Save your program as 2AQ2b.c

TransposeYou are developing a program for a scientific research team that works extensively with matrices. As part of a new project, the team needs a function to calculate the transpose of a given matrix. The transpose of a matrix is obtained by swapping its rows and columns.Your task is to write a C function transposeMatrix that takes a 2D array representing a matrix as input and calculates its transpose.Testcase:Input:1 2 3 4 5 6 7 8 9Output1 4 72 5 83 6 9

Suppose that A and B are n×n matrices. Check the true statements below: A. If det(A) is zero, then two rows or two columns are the same, or a row or a column is zero.B. det(AT)=(−1)det(A)C. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix.D. The determinant of A is the product of the diagonal entries in A

Suppose an array a contains 3 9 6 12. Walk through the following code that swaps two elements in the array.123456789int i = 1;int j = 2;// Good swapdouble temp = a[i];a[i] = a[j];a[j] = temp;// Bad swapa[i] = a[j];a[j] = a[i];Track variables in a trace table. On a sheet of paper, make the table below (the first row is filled in with initial values).i j a[0] a[1] a[2] a[3] temp1 2 3 9 6 12 1)What is the value of temp after line 4 executes?CheckShow answer2)What is the value of a[1] after line 5 executes?CheckShow answer3)What is the value of a[2] after line 6 executes?CheckShow answer4)What is the value of a[1] after line 8 executes?CheckShow answer5)What is the value of a[2] after line 9 executes?CheckShow answer