Matrix Calculator — Linear Algebra Operations

Compute matrix determinant, inverse, multiplication, transpose, addition, and subtraction. Free online calculator for 2x2 and 3x3 matrices with step-by-step examples.

Determinant
Matrix Inverse
Multiplication
Transpose

Matrix Calculator

Perform linear algebra operations on 2x2 and 3x3 matrices

Operations Guide

Determinant

Calculates the determinant value

Inverse (A⁻¹)

Matrix inverse (if determinant ≠ 0)

Transpose (Aᵀ)

Flips matrix across diagonal

Multiplication

Matrix product A × B

Addition/Subtraction

Element-wise operations

How to Use the Matrix Calculator

Getting Started

  1. 1. Choose size: Select 2×2 or 3×3 matrix dimensions
  2. 2. Enter values: Input numerical values in matrix cells
  3. 3. Use examples: Click sample buttons for quick setup
  4. 4. Select operation: Choose from determinant, inverse, etc.
  5. 5. View result: See calculated output with formatting
  6. 6. Copy result: Use copy button to save results

Matrix Operations

Determinant: Scalar value indicating matrix properties
Inverse: Matrix that when multiplied gives identity
Transpose: Matrix with rows and columns swapped
Multiplication: Combines matrices using dot product
Addition/Subtraction: Element-wise operations
Requirements: Inverse requires non-zero determinant

Frequently Asked Questions

What matrix operations can this calculator perform?

This matrix calculator can compute determinant, inverse, multiplication, transpose, addition, subtraction, and scalar multiplication for 2x2 and 3x3 matrices. All operations provide accurate results with proper error handling.

How do I calculate the inverse of a matrix?

Enter your matrix values, then click the "A⁻¹" or "B⁻¹" button. The calculator will compute the inverse matrix if it exists (determinant ≠ 0). If the matrix is not invertible, you'll receive an error message.

Can I multiply matrices of different sizes?

Matrix multiplication is possible when the number of columns in the first matrix equals the number of rows in the second matrix. Our calculator currently supports 2x2 and 3x3 matrix operations with matching dimensions.

What happens if I try to invert a singular matrix?

A singular matrix (determinant = 0) cannot be inverted. The calculator will detect this condition and display an error message: "Matrix is not invertible (determinant = 0)". Check your matrix values for linear dependence.

How accurate are the matrix calculations?

The calculator uses JavaScript's double-precision floating-point arithmetic, providing accuracy to approximately 15-16 significant digits. Results are formatted to 4 decimal places for readability, with automatic cleanup of trailing zeros.