Matrix Calculator — Add, Subtract & Multiply Matrices

Reviewed August 7, 2026

ResultUpdates as you type

Result (1,1)6

Result (1,2)8

Result (2,1)10

Result (2,2)12

Free online matrix calculator for matrix addition, subtraction, multiplication, scalar multiplication, and transpose operations.

Perform 2x2 matrix operations: addition, subtraction, matrix multiplication, scalar multiplication, and transposition.

Understanding Matrix Operations

Matrices are rectangular arrays of numbers arranged in rows and columns used in linear algebra, computer graphics, physics, and statistics.

Supported Operations

Matrix Addition & Subtraction: Performed on matrices of identical dimensions by adding or subtracting corresponding elements.
Matrix Multiplication: Requires that the number of columns in the first matrix equals the number of rows in the second matrix.
Scalar Multiplication: Multiplies every element in the matrix by a real number $k$.
Transpose ($A^T$): Flips a matrix over its diagonal, switching row and column indices.

How to use

Select the matrix operation (Add, Subtract, Multiply, Scalar, Transpose).
Enter the elements of Matrix A and Matrix B.
View the resulting matrix entries instantly.

Formula

Matrix Addition(A + B)_[i,j] = A_[i,j] + B_[i,j]Element-wise addition of corresponding entries.

Matrix Multiplication(A × B)_[i,j] = ∑ A_[i,k] × B_[k,j]Dot product of row i from A and column j from B.

Worked examples

Matrix Addition Example

For A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], A + B = [[6, 8], [10, 12]].

Frequently asked questions

What is matrix multiplication?

Matrix multiplication involves multiplying elements of a row in the first matrix by corresponding elements of a column in the second matrix and summing the products.

What is a transpose matrix?

The transpose of a matrix is formed by swapping its rows and columns.