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A matrix which is formed by turning all the rows of a given matrix into column and vice-versa then the matrix is said to be Transpose matrix. The transpose of matrix A is written as **A ^{T}**

Let us write a C program to Transpose the user entered matrix

c-transpose-matrix.c

#include <stdio.h> int main() { int i, j, row1, row2, col1, col2, a[10][10], b[10][10]; printf("Enter the order of matrix up to (10 x 10): \n "); scanf("%d %d ",&row1, &col1); printf("\nEnter the Elements of matrix A :\n "); for(i = 0;i < row1;i++) { for(j = 0;j < col1;j++) { scanf("%d ",&a[i][j]); } } row2 = col1; col2 = row1; for(i = 0;i < row1;i++) { for(j = 0;j < col1;j++) { b[j][i] = a[i][j]; } } printf("\nThe Matrix Transpose is \n "); for(i = 0;i < row2;i++) { for(j = 0;j < col2;j++) { printf("%4d",b[i][j]); } printf("\n"); } return 0; }

Enter the order of matrix up to (10 x 10) : 3 3 Enter the Elements of matrix A : 1 2 3 4 5 6 7 8 9 The Matrix Transpose is 1 4 7 2 5 8 3 6 9

On seeing line 15 and line 16, we can get clear idea, that column is considered as row whereas row is considered as column.

The above equation shows that the transpose of a transpose matrix is the original matrix.

The above equation shows that when a scalar element is multiplied to a matrix, the order of transposition is irrelevant.

The above equation shows that the transpose of two added matrices is the same as the addition of the two transpose matrices.

The above equation shows that the transpose of a product of matrices equals the product of their transposes in reverse order.

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