Math & Algebra Tool

Matrix Determinant Calculator

Calculate determinants of 2x2 and 3x3 matrices.

Σ The Formula

det(A) for 2x2: ad-bc | det(A) for 3x3: Sarrus rule

Real World Examples

2x2 Matrix
det([1 2; 3 4]) = -2
Identity Matrix
det([1 0; 0 1]) = 1
Singular Matrix
det([1 1; 2 2]) = 0 (No inverse)
3x3 System
Used to solve x, y, z in linear equations

# About This Calculator

A Matrix Determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix.

The determinant tells us important things:
• If det(A) = 0, the matrix is "Singular" and does cannot be inverted (it has no unique solution).
• If det(A) ≠ 0, the matrix has an inverse.
• Geometrically, it represents the scaling factor of the transformation (area for 2D, volume for 3D).

For a 2x2 matrix [[a, b], [c, d]], the determinant is (ad - bc). For 3x3 matrices, the calculation involves specific patterns like the Rule of Sarrus.

This tool instantly calculates the determinant for 2x2 and 3x3 matrices, providing step-by-step logic for the calculation.

How To Use

  1. Select Matrix Size (2x2 or 3x3).
  2. Enter the values into the grid.
  3. Click Calculate Determinant.

Frequently Asked Questions

What is a determinant used for?+

It checks if a matrix is invertible (det != 0) and is used in Cramer's Rule to solve systems of linear equations. It also finds areas/volumes in geometry.

Can I find the determinant of a non-square matrix?+

No. Determinants are defined ONLY for square matrices (2x2, 3x3, etc.).

What does it mean if the determinant is negative?+

It means the orientation of the space has been flipped (like looking in a mirror). The magnitudes (area/volume) are still scaled by the absolute value.

How do I calculate a 3x3 determinant manually?+

Use the Rule of Sarrus (diagonals) or Cofactor Expansion. This tool shows the Rule of Sarrus method.

What is an Identity Matrix?+

A square matrix with 1s on the main diagonal and 0s everywhere else. Its determinant is always 1.

Is Matrix Determinant Calculator free to use?+

Yes, Matrix Determinant Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A Matrix Determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix.

The determinant tells us important things:
• If det(A) = 0, the matrix is "Singular" and does cannot be inverted (it has no unique solution).
• If det(A) ≠ 0, the matrix has an inverse.
• Geometrically, it represents the scaling factor of the transformation (area for 2D, volume for 3D).

For a 2x2 matrix [[a, b], [c, d]], the determinant is (ad - bc). For 3x3 matrices, the calculation involves specific patterns like the Rule of Sarrus.

This tool instantly calculates the determinant for 2x2 and 3x3 matrices, providing step-by-step logic for the calculation.

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