Matrix Calculator

Perform matrix operations including addition, multiplication, determinant, and inverse.

Matrix Calculator

Matrix A

Matrix B

Matrix Operations

Addition
A + B (same dimensions)
Multiplication
A × B (cols of A = rows of B)
Determinant
Square matrices only
Inverse
Square matrices, det ≠ 0

Quick Examples

2×2 Identity Matrix
[1 0; 0 1]
2×2 Determinant
ad - bc for [a b; c d]

About Matrix Operations

A matrix is a rectangular array of numbers arranged in rows and columns. Matrix operations are fundamental in linear algebra and have applications in computer graphics, physics, and engineering.

Matrix Operations

Addition

Add corresponding elements. Matrices must have the same dimensions.

Multiplication

Dot product of rows and columns. A(m×n) × B(n×p) = C(m×p).

Determinant

Scalar value for square matrices. Used to find inverse and solve systems.

Inverse

A⁻¹ such that A × A⁻¹ = I. Only exists if determinant ≠ 0.

Key Properties

  • • Dimensions: m × n (m rows, n columns)
  • • Square Matrix: m = n (same number of rows and columns)
  • • Identity Matrix: Diagonal elements = 1, others = 0
  • • Zero Matrix: All elements = 0
  • • Transpose: Swap rows and columns