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The inverse A⁻¹ satisfies AA⁻¹ = I (identity matrix). Exists only when det(A) ≠ 0. Used to solve systems of equations: Ax=b → x = A⁻¹b.
Guida passo passo
- 1For 2×2: A⁻¹ = (1/det) × [[d,−b],[−c,a]]
- 2For larger: row reduction (Gauss-Jordan elimination)
Esempi risolti
Ingresso
A = [[3,1],[5,2]] · det=1
Risultato
A⁻¹ = [[2,-1],[-5,3]]
Verify: AA⁻¹ = [[1,0],[0,1]] ✓
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