---
title: How to Multiply Matrices
---
## How to Multiply Matrices
The first immportant rule is: the number of columns in matrix A must match number of rows in column B.
The second rule to calculate the product of two matrices is: Line X Column.
The resulting matrix dimension will be rows of first matrix X columns of second matrix.
Let A and B be two matrices of dimension 2, that is, 2 X 2. Their product will be:
The rows of the the resuting matrix is the sum of product of first matrix row elements by second matrix column elements.
#### Example
Let A be a 2 X 3 matrix and B be a 3 X 2 matrix. The product AB will be:
* **Step 1**
* **Step 2**
* **Step 3**
* **Step 4**
#### Attention!
Differently from real numbers algebra, the product AB is not always equal to BA. Calculate it using the example above and find out.
#### More Information:
![Lecture on matrices multiplication](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
![Properties of matrix multiplication](https://www.khanacademy.org/math/precalculus/precalc-matrices/properties-of-matrix-multiplication/a/properties-of-matrix-multiplication)