Matrix Calculator: Add, Multiply & Inverse Online
Start typing to discover tools…
 View all results
Smart Math Tool

Matrix Calculator

Calculate matrix addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication with a clean and accurate online matrix calculator.

Online Matrix Calculator

Choose matrix size, enter values, select operation, and get instant results.

Matrix A

Matrix B

Result

Matrix Operations and Formulas

For addition and subtraction, both matrices must have the same dimensions. Each result cell is found by combining the values in the same row and column position.

(A ± B)ij = aij ± bij

For multiplication, the number of columns in Matrix A must equal the number of rows in Matrix B. Each output cell is the dot product of one row from A and one column from B.

(AB)ij = Σ aikbkj

A determinant and inverse are defined here only for square matrices. An inverse exists only when det(A) ≠ 0; otherwise, the matrix is singular.

Quick Matrix Example

Suppose A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]. Then:

  • A + B = [[6, 8], [10, 12]]
  • A − B = [[−4, −4], [−4, −4]]
  • A × B = [[19, 22], [43, 50]]
  • det(A) = (1 × 4) − (2 × 3) = −2
  • transpose(A) = [[1, 3], [2, 4]]

Use the Fill Example button to test a sample calculation instantly.

Related Math Calculators

Continue your linear algebra and equation work with these free tools:

Algebra Calculator System of Equations Calculator Vector Calculator

What Is a Matrix Calculator?

A matrix calculator is an online math tool that helps you solve matrix operations without doing every row and column calculation manually. It is useful for students, teachers, engineers, programmers, and anyone working with linear algebra.

This Matrix Calculator supports common operations such as addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication. It keeps the interface simple while still giving accurate mathematical output.

Add and Subtract Matrices Quickly combine two matrices of the same size using addition or subtraction.
Multiply Matrices Calculate matrix multiplication when the columns of A match the rows of B.
Transpose, Determinant, and Inverse Find advanced matrix results for square matrices in just a few seconds.

How It Works

Select an operation Choose whether you want to add, subtract, multiply, transpose, find determinant, inverse, or use scalar multiplication.
Choose matrix size Select the number of rows and columns for Matrix A and Matrix B based on your calculation type.
Enter values Type the matrix numbers into each cell. Empty cells are treated as zero for easy input.
Calculate instantly Click the calculate button and the tool will show the final matrix or numerical answer.

Matrix Calculator FAQs

No. Matrix multiplication is only possible when the number of columns in Matrix A equals the number of rows in Matrix B. For example, a 2×3 matrix can multiply with a 3×2 matrix.
This tool supports 2×2, 3×3, and 4×4 matrix sizes. These sizes cover the most common school, college, and practical matrix calculations.
Yes. The calculator can find the inverse of square matrices when the determinant is not zero. If the determinant is zero, the matrix does not have an inverse.
The determinant is a special value calculated from a square matrix. It is often used to check whether a matrix has an inverse and to solve systems of linear equations.
Yes. This Matrix Calculator is free and works directly in your browser without installing extra software.