*3x3 Matrix Multiplication Calculator* is an online tool programmed to perform multiplication operation between the three matrices A and B. Unlike general multiplication, matrix multiplication is not commutative. Multiplying A x B and B x A will give different results. Matrix Multiplication is the most useful and most commonly encountered matrix operation in chemistry applications, but it is more complicated and less intuitive than the operations

### What is Matrix?

A matrix is a rectangular often square array of numbers, or expressions which can be evaluated to numbers. The dimensions m x n refer to the number of rows (m) and columns (n) respectively. The individual values constituting a matrix are called its elements, usually referred to by their row and column numbers, called indices. Matrices have a variety of uses in chemistry, from curve fitting and quantum mechanics to group theory and molecular graphics
There are specific restrictions on the dimensions of matrices that can be multiplied. In the matrix multiplication AB, the number of columns in matrix A must be equal to the number of rows in matrix B. The resulting product matrix will have the same number of rows as matrix A and the same number of columns as B

### 3x3 Matrices Multiplication Formula

### Multiplicative Identity Matrix

The multiplicative identity matrix is a matrix that you can multiply by another matrix and the resultant matrix will equal the original matrix. The multiplicative identity matrix is so important it is usually called the identity matrix, and is usually denoted by a double lined 1, or an **I**, no matter what size the identity matrix is

### Properties of Matrix Multiplication

1. Matrix multiplication is NOT commutative in general

**AB ≠ BA**

2. Matrix multiplication is associative. It doesn't matter how 3 or more matrices are grouped when being multiplied, as long as the order isn't changed

**A(BC) = (AB)C **

3. Matrix multiplication is associative, analogous to simple algebraic multiplication. The only difference is that the order of the multiplication must be maintained

**A(B+C) = AB + AC ≠ (B+C)A = BA + CA **

4. If its a Square Matrix, an identity element exists for matrix multiplication. It is called either E or I

**IA = AI = A**

Matrices are widely used in geometry, physics and computer graphics applications. The array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules. Matrix calculations can be understood as a set of tools that involves the study of methods and procedures used for collecting, classifying, and analyzing data. In many applications it is necessary to calculate 3x3 matrix multiplication where this online 3x3 matrix multiplication calculator can help you to effortlessly make your calculations easy for the respective inputs