Mathematical Tools
Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, transpose, and inverse for 2×2 and 3×3 matrices.
✓ Runs in your browser · Updated 2026-03-31Enter values and click Calculate to see results
Matrix Operations
This calculator supports basic matrix operations for 2×2 and 3×3 matrices.
Determinant
2×2: det = a₁₁·a₂₂ − a₁₂·a₂₁
3×3: det = a₁₁(a₂₂·a₃₃ − a₂₃·a₃₂) − a₁₂(a₂₁·a₃₃ − a₂₃·a₃₁) + a₁₃(a₂₁·a₃₂ − a₂₂·a₃₁)
3×3: det = a₁₁(a₂₂·a₃₃ − a₂₃·a₃₂) − a₁₂(a₂₁·a₃₃ − a₂₃·a₃₁) + a₁₃(a₂₁·a₃₂ − a₂₂·a₃₁)
Inverse Matrix
A matrix has an inverse only if its determinant is non-zero. The inverse satisfies A × A⁻¹ = I (identity matrix).
Singular Matrix
If the determinant equals 0, the matrix is singular and does not have an inverse.
Related Tools
For expression evaluation, try our Scientific Calculator. For statistical operations, use the Standard Deviation Calculator.
Frequently Asked Questions
When can two matrices be multiplied?
Matrix A (m×n) can be multiplied by Matrix B (p×q) only when n = p (columns of A equals rows of B). The result has dimensions m×q.