2x2 Matrix Multiplication Calculator

2x2 Matrix Multiplication Calculator is an online tool programmed to perform multiplication operation between the two matrices A and B. Unlike general multiplication, matrix multiplication is not commutative. Multiplying A x B and B x A will give different results. 2x2 matrices are most commonly employed in describing basic geometric transformations in a 2-dimensional vector space.

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.

2x2 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.

The multiplicative identity matrix obeys the following equation:
IA = AI = A

The multiplicative identity matrix for a 2x2 matrix is:

2x2 Matrices Multiplication Example

The following will show how to multiply two 2x2 matrices:

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 it's 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 2x2 matrix multiplication where this online 2x2 matrix multiplication calculator can help you to effortlessly make your calculations easy for the respective inputs.