doomath Calculator
Matrix Determinant & Inverse Solver
Perform matrix algebra on 3×3 matrices: calculate determinant |A| using cofactor expansion, trace, transpose Aᵀ, and invertible inverse matrix A⁻¹.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSMatrix Determinant & Inverse Solver — Mathematical Derivation & Steps
3 StepsSequential Calculation Breakdown
1
Determinant
Evaluate the 3×3 determinant using cofactor expansion.
2
Trace
Add the three diagonal entries.
3
Inverse test
det(A) is nonzero, so an inverse exists.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Matrix Determinant & Inverse Solver
Perform matrix algebra on 3×3 matrices: calculate determinant |A| using cofactor expansion, trace, transpose Aᵀ, and invertible inverse matrix A⁻¹.
01Set inputsChoose values, units and assumptions.
02Apply the modeldet(A) = a₁₁(a₂₂a₃₃ - a₂₃a₃₂) - a₁₂(a₂₁a₃₃ - a₂₃a₃₁) + a₁₃(a₂₁a₃₂ - a₂₂a₃₁); A⁻¹ = (1/det(A)) adj(A)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter matrix entries across rows 1, 2, and 3. The engine computes the determinant via Laplace cofactor expansion, finds the trace, matrix transpose, and inverted matrix.
Formula & method
det(A) = a₁₁(a₂₂a₃₃ - a₂₃a₃₂) - a₁₂(a₂₁a₃₃ - a₂₃a₃₁) + a₁₃(a₂₁a₃₂ - a₂₂a₃₁); A⁻¹ = (1/det(A)) adj(A)
Assumptions & notes
- A matrix is invertible if and only if its determinant det(A) ≠ 0.
- The trace of a square matrix is the sum of its main diagonal elements.
- det(Aᵀ) = det(A) for all square matrices.