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A⁻¹ undoes A: A·A⁻¹ = I. Computed via adjugate ÷ determinant for 2×2 and 3×3. Singular matrices (det 0) have no inverse and are flagged instead of producing garbage.
Adjugate/determinant inverse; singular matrices flagged.
A⁻¹ = adj(A) / det(A)
| Symbol | Meaning |
|---|---|
| A⁻¹ | Inverse matrix |
[1,2;3,4]⁻¹ = [−2,1;1.5,−0.5] (det −2). Verify: A·A⁻¹ = I.
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Exactly when det = 0 (singular) — rows/columns are dependent.
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Content updated: September 2026