# Matrices

1. What is matrix multiplication?

Matrix multiplication refers to the process of multiplying two matrices together. Matrix multiplication is a fundamental operation in linear algebra and is often referred to as matrix multiplication. In mathematics, matrix multiplication is defined as the product of the elements of two matrices. In computer science, matrix multiplication is the process of multiplying two n-dimensional arrays (or matrices) together.

2. Why do we need matrix multiplication?

In order to understand what matrix multiplication is, let's first look at how we multiply numbers. If we want to multiply 2x3, we would simply multiply each number individually. So if we wanted to multiply 2x3 6x3, we would have to multiply 2 x 3 6 x 3. However, if we were to multiply 2x3 using matrix multiplication, we could just add them together. So if we wanted 2x3 + 3x2 6x3, then we would have to multiply the 2x3 by 1/3 and add the 3x2 by -1/3. So we would end up with 2x3 + 3(1/3)x2 6x2 + (-1/3)x3. Now, if we wanted to multiply 4x5, we would have to add them together. So we would have to multiply 4x5 20x5. But if we were to use matrix multiplication, we could take the 4x5 and multiply it by 5. So we would have 4x5 * 5 40x5.

3. How does matrix multiplication work?

The way matrix multiplication works is similar to how we multiply numbers. We start off by taking the first row of the first matrix and adding it to the second row of the second matrix. Then we move down to the third row of the first matrix, and add it to the fourth row of the second matrix, and so on until we reach the last row of the first matrix. Once we've added all of the rows of the first matrix to the corresponding rows of the second matrix, we repeat the same process for the second matrix. When we're done, we'll have the result of the matrix multiplication.

4. How do we calculate the transpose of a matrix?

If you're familiar with matrix multiplication, you know that A*B AB. Well, the transpose of a square matrix is its inverse. So if we took our example above, we would have: