⬛ Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, inverse, and transpose
Matrix Settings
Matrix A
Matrix B
How to Use This Calculator
- Choose the matrix size (2×2 or 3×3)
- Select the operation you want to perform
- Enter the values for Matrix A (and Matrix B if needed for the operation)
- Click "Calculate" to see the result
- Review the calculated matrix and any additional information
Understanding Matrix Operations
Addition & Subtraction
Matrices can be added or subtracted only if they have the same dimensions. Each element is added or subtracted from the corresponding element in the other matrix.
Multiplication
Matrix multiplication is not commutative (A×B ≠ B×A). The element at position (i,j) in the result is the dot product of row i from matrix A and column j from matrix B.
Determinant
The determinant is a scalar value that can be computed from a square matrix. It has important properties in linear algebra and is used to determine if a matrix is invertible.
Inverse
The inverse of a matrix A is another matrix A⁻¹ such that A×A⁻¹ = I (identity matrix). A matrix is invertible only if its determinant is non-zero.
Transpose
The transpose of a matrix is obtained by swapping its rows and columns. If A is m×n, then A^T is n×m.
Frequently Asked Questions
How accurate is the matrix calculator?
This tool uses standard matrix algorithms to ensure accuracy. Due to floating-point arithmetic, very small numbers may have minor rounding errors.
Can I calculate larger matrices?
Currently, this calculator supports 2×2 and 3×3 matrices, which cover most common use cases in algebra and introductory linear algebra courses.
What if my matrix has no inverse?
A matrix has no inverse if its determinant is zero (it's called a singular matrix). The calculator will display an error message in this case.
Is this tool free to use?
Yes! This tool is completely free with no hidden costs, subscriptions, or limitations. Use it as often as you need.
Is my data private?
Absolutely. All processing happens locally in your browser. Your data never leaves your device and is not stored on any server.