In Python, we can implement a matrix as a nested list (list inside a list). We can treat each element as a row of the matrix.

For example `X = [[1, 2], [4, 5], [3, 6]]`

would represent a 3x2 matrix. The first row can be selected as `X[0]`

. And, the element in the first-row first column can be selected as `X[0][0]`

.

Transpose of a matrix is the interchanging of rows and columns. It is denoted as `X'`. The element at `ith` row and `jth` column in `X` will be placed at `jth` row and `ith` column in `X'`. So if `X` is a 3x2 matrix, `X'` will be a 2x3 matrix.

Here are a couple of ways to accomplish this in Python.

## Matrix Transpose using Nested Loop

```
# Program to transpose a matrix using a nested loop
X = [[12,7],
[4 ,5],
[3 ,8]]
result = [[0,0,0],
[0,0,0]]
# iterate through rows
for i in range(len(X)):
# iterate through columns
for j in range(len(X[0])):
result[j][i] = X[i][j]
for r in result:
print(r)
```

**Output**

[12, 4, 3] [7, 5, 8]

In this program, we have used nested `for`

loops to iterate through each row and each column. At each point we place the `X[i][j]` element into `result[j][i]`.

## Matrix Transpose using Nested List Comprehension

```
''' Program to transpose a matrix using list comprehension'''
X = [[12,7],
[4 ,5],
[3 ,8]]
result = [[X[j][i] for j in range(len(X))] for i in range(len(X[0]))]
for r in result:
print(r)
```

The output of this program is the same as above. We have used nested list comprehension to iterate through each element in the matrix.