Matrix Mathematics & Determinant Calculator

Perform 2x2, 3x3, and 4x4 matrix Addition, Subtraction, Multiplication, Determinant, Transpose, and Inverse calculations.

Matrix Mathematics & Determinant Calculator

Perform 2x2, 3x3, and 4x4 matrix Addition, Subtraction, Multiplication, Determinant, Transpose, and Inverse calculations.

Dimensions:

Matrix A:

Matrix B:

Calculation Output:

About This Tool

The Matrix Mathematics Calculator performs linear algebra calculations on 2x2, 3x3, and 4x4 square matrices with instant determinant, matrix transposition, inversion, and matrix multiplication.

Key Features

Supports 2x2, 3x3, and 4x4 matrix sizes

Calculates Matrix Addition (A + B), Subtraction (A - B), and Multiplication (A × B)

Calculates Determinant det(A), Transpose Aᵀ, and Inverse A⁻¹

Step-by-step determinant expansion

How to Use This Tool

Select matrix dimension (2x2, 3x3, or 4x4).
Enter the scalar values for Matrix A and Matrix B.
Select the desired operation (A + B, A × B, det(A), Aᵀ, Inverse).
View the resulting output matrix.

Why Use This Tool

Compute 3D graphics transformation matrices (rotation, translation, projection).
Solve systems of linear equations in physics and engineering.
Verify machine learning linear algebra calculations.

Pro Tips

A matrix has an Inverse A⁻¹ if and only if its Determinant is non-zero (det(A) ≠ 0).

Frequently Asked Questions

When does a matrix have an inverse?

A square matrix has an inverse if and only if its determinant is non-zero (det(A) ≠ 0). Matrices with zero determinants are called singular.

Is matrix multiplication commutative (A × B = B × A)?

No, matrix multiplication is generally non-commutative; A × B is almost never equal to B × A.

Matrix Mathematics & Determinant Calculator