Determinant Calculator
Calculate the determinant of any n×n matrix with full cofactor expansion steps. Supports 2×2 up to large matrices.
Calculate Determinant →✓ Free · No Signup · No Paywall · Step-by-Step
Free Matrix Solvers
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Industry-level matrix computation for students, engineers and researchers. Get full step-by-step working with professional KaTeX rendering — completely free.
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Core Matrix Calculators
The most-used tools for linear algebra, fully functional with step-by-step solutions.
Eigenvalue & Eigenvector
Find all eigenvalues and eigenvectors with characteristic polynomial derivation and step-by-step solution.
Find Eigenvalues →RREF Calculator
Reduce any matrix to Row Echelon Form with complete Gaussian elimination steps shown for every row operation.
Get RREF →Inverse Matrix Calculator
Find the inverse of any invertible matrix using Gauss-Jordan elimination with full working shown.
Invert Matrix →Matrix Multiplication
Multiply matrices of compatible dimensions with element-by-element computation shown for every result cell.
Multiply Matrices →Gram-Schmidt Calculator
Orthogonalize and orthonormalize any set of vectors using the Gram-Schmidt process with full steps.
Orthogonalize →Transpose Calculator
Transpose any matrix instantly. See step-by-step row-to-column swaps with properties verification.
Transpose →Matrix Rank Calculator
Find the rank of any matrix using RREF. Shows pivot identification and null space dimension.
Find Rank →Cross Product Calculator
Compute the cross product of two 3D vectors with geometric interpretation and magnitude calculation.
Cross Product →Advanced Decomposition Tools
Professional-grade factorizations and solvers for advanced linear algebra.
Linear System Solver
Solve Ax = b systems with Gaussian elimination, Cramer's rule and consistency checks.
Solve System →LU Decomposition
Factor any matrix A = LU with partial pivoting. Shows L and U matrices with all elimination steps.
LU Decompose →QR Decomposition
Compute A = QR where Q is orthogonal and R is upper triangular. Via Gram-Schmidt with steps.
QR Decompose →SVD Calculator
Singular Value Decomposition A = UΣVᵀ. Outputs singular values, U, Σ, and V matrices.
Compute SVD →Matrix Power Calculator
Raise any square matrix to any integer power. Efficient algorithm with full multiplication trace.
Matrix Power →Matrix Addition
Add or subtract two matrices element-by-element with dimension compatibility checking.
Add Matrices →Practice & Learning Tools
Sharpen your skills with daily challenges, quizzes and printable worksheets.
Problem of the Day
A fresh matrix challenge every day. Build a daily solving habit and track your streak.
Today's Challenge →Matrix Quiz
Test your knowledge with timed multiple-choice questions on all matrix topics.
Take Quiz →Worksheet Generator
Generate printable practice worksheets for determinants, inverses, eigenvalues, and more.
Generate →Matrix Glossary
Definitions of every linear algebra term, from adjugate to zero matrix with examples.
Browse Glossary →Why MatrixSolverOro?
Industry-Level Accuracy
Powered by math.js with custom step-by-step algorithms. Results verified against established mathematical methods for n×n matrices of any size.
Professional KaTeX Rendering
All equations and step-by-step solutions render using KaTeX — the gold standard for math in browsers. Results look like textbook quality.
No Signup. No Paywall. Ever.
Every tool, every feature, every step-by-step solution is completely free. No account creation, no premium tier required.
Works on Any Device
Fully responsive design works perfectly on phones, tablets and desktops. Solve matrix problems anywhere, anytime.
Frequently Asked Questions
Most calculators support matrices from 1×1 up to 10×10 (and larger for basic operations). The eigenvalue calculator supports up to 6×6 for guaranteed accuracy. You can manually enter any size using the row/column selectors.
Yes — completely free. No signup, no login, no premium plan, no watermarks. All 15+ calculators with full step-by-step solutions are available at no cost.
Yes. Enter any real number: integers (5), decimals (3.14), or fractions as decimals (0.5 for ½). The calculator handles all standard real number inputs.
We use math.js — a high-precision JavaScript mathematics library — combined with our own step-by-step algorithms. Results are verified to standard floating-point precision (up to 10 significant figures) with intelligent rounding to remove numerical noise.