Matrix Determinant Calculator

Free Client-Side Step-by-Step

Teacher/student friendly determinant solver: enter fractions like 1/2, choose method, and get readable step-by-step reasoning. 100% client-side with support for 2×2 to 10×10.

Matrix Input
Supports 2×2 up to 10×10 square matrices
Text mode supports paste. Grid mode is compact for quick edits. Fractions like -7/11 are supported.
Classroom tip: For triangular matrices, determinant is product of diagonal entries. Use Cofactor mode for small matrices to see formula expansion.
Result
Enter a square matrix and click "Calculate Determinant" to see a teacher-style solution card.
Step-by-Step Solution
Unified lesson playback appears here after calculation.

Exam-Style Practice

About This Matrix Determinant Tool & Methodology

The determinant det(A) is a scalar computed from a square matrix. Key properties: det(I)=1, det(AB)=det(A)×det(B), det(AT)=det(A). If det(A)=0 the matrix is singular (not invertible). This tool computes det(A) using LU decomposition, cofactor expansion, or Gaussian elimination. All calculations run client-side—no data stored.

Authorship & Expertise

  • Author: Anish Nath
  • Background: Math and developer tools for education
  • Methods: LU, cofactor expansion, Gaussian elimination

Trust & Privacy

  • Privacy: All calculations run locally; no data stored
  • Client-side: Your matrices never leave your device
  • Support: @anish2good

Matrix Determinant: FAQ

How do I calculate the determinant of a matrix?

Enter a square matrix and click Calculate. The tool shows step-by-step methods such as cofactor expansion and row operations; for larger sizes it may use LU decomposition for efficiency.

What sizes and methods are supported?

This calculator supports square matrices from 2×2 up to 10×10 and can display cofactor expansion steps, row-operation reductions, and LU-based computations.

What does det(A) = 0 mean?

det(A) = 0 indicates the matrix is singular: rows/columns are linearly dependent, rank is less than n, and A is not invertible.

Can I practice with exam-style determinant questions?

Yes. The Exam-Style Practice section generates problems at Easy (2×2), Medium (3×3), or Hard (4×4 and singularity checks) with instant scoring and answer reveal.

What are useful properties of determinants?

Key properties: det(AB) = det(A)det(B), det(A^T) = det(A), det(cA) = c^n det(A) for n×n, swapping rows flips the sign, and a row of zeros makes det = 0.

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