逆矩阵计算器 — 公式

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)