Matrix Calculator
Add, subtract, multiply, transpose, or find the determinant of matrices. Choose your matrix sizes, enter the values, and get an instant result.
Recommended Settings
Pro Tips
- •Matrix addition and subtraction require both matrices to have identical dimensions
- •Matrix multiplication requires the number of columns in A to match the number of rows in B - the result takes A's row count and B's column count
- •Only square matrices (same number of rows and columns) have a determinant
- •Transposing a matrix flips it over its diagonal, turning rows into columns
Most Popular
Most users start with 2×2 or 3×3 matrices for linear algebra coursework
When to Use This Tool
Check matrix arithmetic, determinants, or transpositions for a linear algebra course.
Understand how matrix multiplication combines or transforms sets of values, such as in computer graphics or data science.
Perform matrix operations that come up in systems of equations, circuit analysis, or structural calculations.
Double-check a matrix operation you worked out by hand.
How It Works
Enter the dimensions and values for matrix A (and matrix B, if the operation requires it)
Addition and subtraction combine corresponding entries directly, entry by entry
Multiplication computes each result entry as the dot product of a row from A and a column from B
The determinant is calculated using row reduction (Gaussian elimination) for larger matrices, or the direct formula for 1×1 and 2×2 matrices
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Files never leave your device. All processing happens locally in your browser.
Lightning Fast
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Open Source
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Frequently Asked Questions
Why do I get a dimension mismatch error?
Addition and subtraction require both matrices to be exactly the same size. Multiplication requires the number of columns in matrix A to equal the number of rows in matrix B. Adjust your matrix sizes to satisfy these rules.
What is a determinant used for?
The determinant is a single number computed from a square matrix that indicates properties like whether the matrix is invertible (a determinant of zero means it isn't) and how the matrix scales area or volume.
How large can my matrices be?
This tool supports matrices up to 4×4. Larger matrices are typically handled with specialized numerical software rather than a general-purpose browser tool.
Is my data sent to a server?
No. All calculations happen instantly in your browser using JavaScript. Nothing you enter is transmitted anywhere.
Is matrix multiplication the same as multiplying element by element?
No. Standard matrix multiplication computes each output entry as a dot product of a row and column, not by multiplying matching positions directly. That's a different operation sometimes called the Hadamard product.