Matrix Calculator
Visual matrix math with step-by-step solutions. Up to 5x5 matrices, seven operations.
Matrix A
Matrix B
Result
History (last 5)
Frequently Asked Questions
How do I multiply two matrices?
Enter your matrices into ML3X, select the A x B operation, and click Calculate. The matrix calculator shows the result and a step-by-step breakdown of each element calculation. For multiplication to work, the number of columns in Matrix A must equal the number of rows in Matrix B.
How do I calculate the determinant of a matrix?
Enter your square matrix and select det(A). ML3X uses cofactor expansion along the first row and shows every intermediate step. It supports matrices up to 5x5. A determinant of zero means the matrix is singular and has no inverse.
Can ML3X compute eigenvalues?
Yes. ML3X computes eigenvalues for square matrices up to 5x5. For 2x2 matrices it uses the quadratic formula, for 3x3 it uses Cardano's formula handling all three root cases. The display shows the characteristic polynomial so you can verify the computation.
How do I find the inverse of a matrix?
Enter your square matrix, select the inverse operation, and click Calculate. ML3X uses the adjugate method (adjugate divided by determinant) which makes the step-by-step display clear and educational. If the determinant is zero, no inverse exists.
What is the maximum matrix size supported?
ML3X supports matrices up to 5x5 for all operations. The determinant algorithm uses cofactor expansion which is O(n!) but runs instantly at this size. For larger matrices, consider NumPy or MATLAB. The 5x5 limit covers most homework problems and quick engineering checks.
Is my data saved anywhere?
ML3X keeps a history of your last 5 calculations in browser memory for quick reference. Nothing is persisted across page loads and no data is ever sent to a server. The entire matrix calculator runs in your browser with zero network requests.
How ML3X Works
ML3X is a free, browser-based matrix calculator designed for students, engineers, and developers who need to perform linear algebra operations with full transparency into the math. Unlike black-box calculators that only show the final answer, ML3X displays step-by-step solutions for every operation, making it both a computation tool and a learning aid. You can add, subtract, and multiply matrices up to 5x5, compute determinants, find matrix inverses, and calculate eigenvalues — all with detailed intermediate calculations visible on screen.
The calculator supports seven operations: addition (A + B), subtraction (A - B), multiplication (A x B), transpose, determinant, inverse, and eigenvalue computation. For matrix multiplication, every element of the result matrix shows the dot product calculation that produced it. For determinants, the cofactor expansion is displayed row by row. The inverse computation uses the classical adjugate method (adjugate matrix divided by determinant), chosen over Gaussian elimination specifically because it produces a clearer step-by-step display for educational purposes.
Eigenvalue computation is the most mathematically complex feature. For 2x2 matrices, ML3X solves the characteristic polynomial using the quadratic formula. For 3x3 matrices, it uses Cardano's formula, correctly handling all three cases: three distinct real roots, one real root with a complex conjugate pair, and repeated roots. The characteristic polynomial is displayed so users can verify the computation independently.
Features
ML3X provides matrix addition and subtraction with element-wise step display, matrix multiplication with full dot-product breakdown for each result element, transpose visualization, determinant computation via cofactor expansion with all minors shown, matrix inverse using the adjugate method with step-by-step cofactor and adjugate display, eigenvalue calculation with characteristic polynomial, and a calculation history storing the last 5 operations for quick reference. The matrix inputs include random fill, clear, and identity matrix buttons for fast setup.
Who Uses This
ML3X is built for linear algebra students who need to verify homework solutions and understand the computation process, machine learning engineers checking dimension arithmetic before implementing matrix operations in code, data scientists working with covariance matrices, PCA, and other linear algebra-heavy analyses, and software developers who need quick matrix calculations without opening MATLAB or a Python notebook. If you work with neural network layers and need to trace tensor shapes through your architecture, HeyTensor provides a dedicated tensor shape calculator. For time-based computations and cron scheduling, EpochPilot offers epoch conversion and timezone tools. General developer utilities like Base64 encoding and JWT decoding are available at KappaKit.
Privacy
All matrix calculations run locally in your browser. No matrix data, computation results, or history entries are sent to any server. The source code is open on GitHub. There are no cookies, no analytics scripts, and no tracking of any kind.
Contact
ML3X is built and maintained by Michael Lip. For questions or feedback, email support@zovo.one or visit the project on GitHub.