Matrix Calculator

What Is a Matrix Calculator?

A matrix calculator is an online mathematical tool for performing calculations involving matrices. A matrix is a rectangular arrangement of numbers organised into rows and columns. Matrices are widely used in algebra, statistics, computer science, engineering, physics, economics and other areas of mathematics.

This free matrix calculator provides several common matrix operations without requiring specialist mathematical software. Enter the values for one or two matrices, choose the required operation and the calculator will produce the result directly in your browser.

Why Use the Matrix Calculator?

The calculator provides several frequently used matrix operations in one interface, making it suitable for checking calculations, studying linear algebra and working with numerical matrix data.

How to Use the Matrix Calculator

Enter your matrix values and select the mathematical operation you need. The calculator validates the dimensions automatically before performing the calculation.

1. Choose the dimensions. — Select the number of rows and columns for Matrix A and Matrix B.
2. Enter the values. — Type a number into each cell of the required matrix.
3. Select an operation. — Choose addition, subtraction, multiplication, determinant, inverse, transpose or RREF.
4. Review the result. — The calculated matrix or scalar result will appear immediately below the controls.

Matrix Calculations Explained

Matrix addition and subtraction can only be performed when the two matrices have the same number of rows and columns. Each corresponding pair of elements is added or subtracted to create a new matrix with the same dimensions.

Matrix multiplication follows different rules. If Matrix A has m rows and n columns, and Matrix B has n rows and p columns, their product is possible and produces an m × p matrix. Each value in the resulting matrix is calculated by multiplying the appropriate row from A by the appropriate column from B and adding the products.

What Is a Matrix Determinant?

The determinant is a single numerical value associated with a square matrix. It provides information about properties such as whether a matrix is singular and whether it has an inverse. A square matrix has an inverse only when its determinant is non-zero.

What Is a Matrix Inverse?

The inverse of a square matrix A is another matrix, written A⁻¹, that satisfies A × A⁻¹ = I, where I is the identity matrix of the same size. An inverse exists only when the original square matrix is non-singular, meaning its determinant is not zero.

Matrix Calculator Accuracy and Limitations

The calculator performs its calculations locally in your web browser using JavaScript. Matrix values can be entered as integers, decimals and negative numbers. Numerical results are rounded to a practical number of decimal places for display.

Addition and subtraction require matrices with identical dimensions. Matrix multiplication requires compatible dimensions, while determinant and inverse calculations require square matrices. A matrix with a zero determinant does not have an ordinary matrix inverse.

Frequently Asked Questions