🎓 Mathematics • Linear Algebra
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Matrix Calculator
Solves 2x2 and 3x3 matrix addition, subtraction, dot product multiplication, determinants, transposes, and matrix inverses.
Dimensions:
Presets:
Matrix A (3 × 3)
Matrix B (3 × 3)
Matrix Product (A × B)
4
0
6
1
-5
6
16
18
7
What is a Matrix?
A matrix is a rectangular grid of numbers arranged in rows and columns.
Matrices represent linear transformations, systems of linear equations, and 3D graphics rotations.
Formula & Step-by-Step Calculation
C = A × B, det(A), A⁻¹ = (1 / det(A)) × adj(A)
Matrix multiplication row-by-column dot product and inverse.
Worked Step-by-Step Examples
Example 1
Multiply two 2x2 identity matrices
Solution: Identity Matrix I
• I × I = I
Common Real-World & Academic Use Cases
- ✓ 3D computer graphics transformations
- ✓ Solving systems of differential equations
- ✓ Quantum state vectors
How to Use the Matrix Calculator
1
Input Matrices A & B
Fill in numerical grid entries.
2
Select Operation
Choose Add, Multiply, Invert, or Transpose.
3
Review Matrix Result
Inspect resulting matrix and determinant.
Frequently Asked Questions
Q: When does a matrix have an inverse?
Only square matrices with a non-zero determinant (det(A) ≠ 0) possess an inverse.