Matrix Calculator
Perform matrix addition, subtraction, multiplication, transpose, and determinant for 2×2 and 3×3 matrices. Full matrix calculator. Free.
Matrix Calculator
toolznova.com • Free Calculator
How to Use
Calculate matrices in 3 steps.
Choose Operation
Select add, subtract, multiply, determinant, or transpose.
Enter Matrix Values
Fill in the values for Matrix A (and B if needed).
Get Result
Click Calculate to see the resulting matrix or value.
Why ToolzNova?
Instant
Results in milliseconds.
Accurate
Precise formulas every time.
Private
No data sent anywhere.
Everywhere
Mobile, tablet, desktop.
Why Use Matrix Calculator?
- Linear Algebra: Matrices are fundamental to linear algebra courses.
- Systems of Equations: Solve linear systems using matrix operations.
- Computer Graphics: Transformations (rotation, scaling) use matrices.
- Machine Learning: Neural networks use matrix multiplication extensively.
- Physics: Quantum mechanics and mechanics use matrix representations.
- Engineering: Structural analysis and circuit analysis use matrices.
Tips & Examples
- Matrix addition/subtraction: add/subtract corresponding elements.
- Matrix multiplication: row of A × column of B — not element-wise!
- Order matters in multiplication: A×B ≠ B×A (not commutative).
- Determinant = 0 means matrix is singular and not invertible.
- Transpose: flip rows and columns — element (i,j) becomes (j,i).
- 2×2 determinant: ad − bc for matrix [[a,b],[c,d]].
Free Matrix Calculator Online
ToolzNova's free matrix calculator performs addition, subtraction, multiplication, determinant, transpose, and scalar multiplication for 2×2 and 3×3 matrices. Results displayed in a formatted matrix grid.
Matrices are rectangular arrays of numbers used in linear algebra, computer graphics, machine learning, and engineering. Matrix operations are fundamental to solving systems of equations and transforming data.
Matrix Operation Formulas
Addition: (A+B)ᵢⱼ = Aᵢⱼ+Bᵢⱼ. Multiplication: (AB)ᵢⱼ = Σ Aᵢₖ×Bₖⱼ. 2×2 Det: ad−bc. Transpose: (Aᵀ)ᵢⱼ = Aⱼᵢ.