Inverse Matrix Calculator
Calculate the inverse of a 2×2 or 3×3 matrix. See the determinant, adjugate matrix, and the resulting inverse with step-by-step explanation.
How to Use the Inverse Matrix Calculator
- Enter the numbers or values in the input fields.
- The result is calculated and displayed automatically.
- Review the step-by-step solution or detailed breakdown.
- Copy the result or adjust inputs for a new calculation.
Référence rapide
| De | Vers |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
Cas d'utilisation
- •Checking homework or exam answers quickly and accurately.
- •Verifying manual calculations in professional or academic work.
- •Learning mathematical concepts with instant visual feedback.
- •Performing quick computations during meetings or presentations.
Formule
For a 2×2 matrix [[a,b],[c,d]]: A⁻¹ = (1/det)·[[d,−b],[−c,a]]. For a 3×3 matrix: A⁻¹ = (1/det)·adj(A), where adj(A) is the transpose of the cofactor matrix. The inverse exists only when det(A) ≠ 0.
Questions fréquemment posées
What is an inverse matrix?
The inverse of a matrix A is a matrix A⁻¹ such that A·A⁻¹ = A⁻¹·A = I (the identity matrix). It exists only for square matrices with non-zero determinant.
What does it mean if a matrix is singular?
A singular matrix has determinant zero and no inverse. It means the rows or columns are linearly dependent, and the corresponding system of equations has no unique solution.
How is the adjugate matrix computed?
The adjugate (classical adjoint) is the transpose of the cofactor matrix. Each cofactor is the signed minor: C(i,j) = (−1)^(i+j) · det(M(i,j)), where M(i,j) is the submatrix with row i and column j removed.