Back to Tools
Matrix Calculator
ο»Ώ
About the Matrix Calculator
Add, subtract and multiply 2Γ2 or 3Γ3 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 4Γ6 β 7Γ2 = 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 Γ B equals B Γ A.
Tips
- Matrix multiplication is not commutative: A Γ B is usually different from B Γ A.
- Only matrices of the same size can be added.
Frequently Asked Questions
When its determinant is zero (a singular matrix).
Only when it is square and its determinant is not zero.
A square matrix with ones on the diagonal and zeros elsewhere. Multiplying by it leaves a matrix unchanged.