Matrix Calculator: Add, Multiply & Invert Matrices Online
Perform matrix arithmetic: multiplication, addition, determinants, transposes, and matrix inversion with step-by-step working.
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How to Use the Matrix Calculator: Matrix Multiplication & Determinants
- 1Choose matrix dimensions (2x2, 3x3).
- 2Enter matrix elements.
- 3Select operation (Multiply, Determinant, Inverse).
Formula & How It Works
Linear Algebra Matrix Product
Computes dot product of row i with column j: C_ij = Σ A_ik × B_kj.
Worked Examples
2x2 Determinant Calculation
Input: [[4, 2], [3, 1]]
Explanation: Calculates ad - bc.
Frequently Asked Questions
Can non-square matrices have a determinant?▼
No, determinants are strictly defined only for square (n × n) matrices.
Quick Reference & Conversion Table
| Operation | Requirement | Formula |
|---|---|---|
| Multiplication (A × B) | Cols(A) == Rows(B) | Row · Column Dot Products |
| Determinant 2x2 | Square matrix | ad - bc |
| Transpose (Aᵀ) | Any matrix | Swap rows with columns |
⚠️ Common Pitfalls to Avoid
- •Attempting matrix multiplication where columns of A do not equal rows of B.
💡 Practical Real-World Uses
- •Computer graphics 3D transformations, physics stress tensors, and machine learning neural networks.
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