Free & Instant
Matrix Calculator
Add, subtract, or multiply 2×2 or 3×3 matrices instantly.
Matrix Calculator
Choose matrix size, enter values, and pick an operation.
Matrix A
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Matrix B
Result Matrix
What is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns, used extensively in linear algebra, computer graphics, engineering, and data science for representing and transforming data.
Matrix Operation Formulas
Addition/Subtraction: Add or subtract corresponding elements (same size matrices only)
Multiplication: Row of A × Column of B, summed for each position
Frequently Asked Questions
Why does matrix multiplication work differently than addition?
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Matrix multiplication combines rows of the first matrix with columns of the second, following specific rules — it's not simply multiplying corresponding elements like addition does.
Does matrix multiplication order matter?
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Yes, unlike regular number multiplication, A × B usually doesn't equal B × A for matrices — order matters significantly.
Can I multiply matrices of different sizes?
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Only if the number of columns in the first matrix equals the number of rows in the second. This calculator works with equal-sized 2×2 or 3×3 matrices for all three operations.
Where are matrices used in real life?
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Matrices are fundamental in computer graphics (3D transformations), machine learning (data representation), physics (systems of equations), and cryptography.