Matrix Inverse Calculator (2×2) — Formule
## 2×2 Matrix Inverse
### Formula
For matrix A = [[a, b], [c, d]] with det ≠ 0:
**A⁻¹ = (1/det) × [[d, -b], [-c, a]]**
where det = ad - bc.
### Steps
1. Calculate the determinant
2. Swap a and d
3. Negate b and c
4. Divide every element by the determinant
### Verification
A × A⁻¹ = I (identity matrix)
### Formula
For matrix A = [[a, b], [c, d]] with det ≠ 0:
**A⁻¹ = (1/det) × [[d, -b], [-c, a]]**
where det = ad - bc.
### Steps
1. Calculate the determinant
2. Swap a and d
3. Negate b and c
4. Divide every element by the determinant
### Verification
A × A⁻¹ = I (identity matrix)
Exemple Résolu
Find the inverse of [[4, 7], [2, 6]].
- det = 4×6 - 7×2 = 24 - 14 = 10
- Inverse = (1/10) × [[6, -7], [-2, 4]]
- = [[0.6, -0.7], [-0.2, 0.4]]