Matrix Determinant Calculator

Use our free matrix determinant calculator to compute the determinant of any square matrix, with step-by-step expansion for 2×2 and 3×3 matrices.

Math

Matrix

Formula

The determinant of a square matrix is a scalar value that encodes important properties. A zero determinant means the matrix is singular (no inverse). Uses Laplace expansion for computation.

det(A) = Σⱼ (−1)^{1+j} × a₁ⱼ × det(M₁ⱼ)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter a square matrix (rows separated by ;, columns by ,).
2Click Calculate to compute the determinant.
3For 2×2: ad − bc. For 3×3: Sarrus' rule or Laplace expansion.

Examples

2×2

1.det = 4×8 − 6×3 = 32−18 = 14
2.det ≠ 0 → non-singular

Result: 14

3×3

1.Laplace expansion along row 1
2.det = 1×(1×0−4×6) − 2×(0×0−4×5) + 3×(0×6−1×5)

Result: 1

Singular 2×2

1.det = 2×2−4×1 = 4−4 = 0
2.det = 0 → singular, no inverse

Result: 0

Frequently Asked Questions

A scalar that summarizes the matrix. Zero = singular.

det = ad − bc for [[a,b],[c,d]].

The matrix is singular (no inverse, linearly dependent rows/columns).

The matrix is invertible (non-singular).

Recursive method: sum of elements × cofactors along a row or column.

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CalculateMe Team

Last updated: 2026-07-14

Matrix Determinant Calculator

Formula

How It Works

Examples

2×2

3×3

Singular 2×2

Frequently Asked Questions

What is a determinant?

2×2 formula?

What does det = 0 mean?

What does det ≠ 0 mean?

What is Laplace expansion?

Related Calculators

Matrix Determinant Calculator

Formula

How It Works

Examples

2×2

3×3

Singular 2×2

Frequently Asked Questions

What is a determinant?

2×2 formula?

What does det = 0 mean?

What does det ≠ 0 mean?

What is Laplace expansion?

Related Calculators