matrix operations in python without numpy

Certainly! Let's create a simple tutorial on basic matrix operations in Python without using NumPy. We'll cover matrix addition, subtraction, multiplication, and transpose. For this tutorial, I'll assume you have some basic knowledge of Python.
Matrix operations are fundamental in linear algebra and many scientific computing applications. While NumPy is a powerful library for numerical operations in Python, it's useful to understand the basic concepts without relying on external libraries. In this tutorial, we'll explore matrix operations using native Python lists.
Before diving into operations, let's understand how we can represent matrices using Python lists. A matrix is a 2D array, and we can use nested lists to represent it. Each list inside the outer list represents a row of the matrix.
Matrix addition is performed by adding corresponding elements of two matrices. Matrices must have the same dimensions for addition to be valid.
Similar to addition, matrix subtraction is performed by subtracting corresponding elements of two matrices with the same dimensions.
Matrix multiplication involves multiplying elements and summing the results. The number of columns in the first matrix must be equal to the number of rows in the second matrix.
Transposing a matrix involves switching its rows and columns.