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Matrix Calculator
Add, subtract and multiply 2×2 or 3×3 matrices, and find determinants, transposes and inverses.
About the Matrix Calculator
Add, subtract and multiply 2×2 or 3×3 matrices, and find determinants, transposes and inverses.
How to use the Matrix Calculator
- Choose the Matrix Size (2x2 or 3x3) and press Update Matrix Size.
- Select an Operation: addition, subtraction, multiplication, determinant, transpose or inverse.
- Enter the numbers in Matrix A (and Matrix B where needed) and press Calculate.
Formula and method
Addition and subtraction work entry by entry. Multiplication combines rows of A with columns of B. The inverse exists only if the determinant is not zero.
Worked example
The determinant of [[4, 7], [2, 6]] is 4×6 − 7×2 = 10, so the matrix is invertible.
When to use the Matrix Calculator
- Adding, multiplying and inverting matrices for linear algebra homework.
- Solving systems of linear equations.
- Working with transformations in graphics and engineering.
Common mistakes to avoid
- Multiplying matrices of incompatible sizes. The columns of the first must equal the rows of the second.
- Assuming A × B equals B × A.
Tips
- Matrix multiplication is not commutative: A × B is usually different from B × A.
- Only matrices of the same size can be added.
Frequently asked questions
When does a matrix have no inverse?
When its determinant is zero (a singular matrix).
When does a matrix have an inverse?
Only when it is square and its determinant is not zero.
What is the identity matrix?
A square matrix with ones on the diagonal and zeros elsewhere. Multiplying by it leaves a matrix unchanged.