Matrix Inverse Calculator (2×2) Formula
Understand the math behind the matrix inverse calculator (2×2). Each variable explained with a worked example.
Formulas Used
Determinant
determinant = detInv A
inv_a = det != 0 ? d / det : 0Inv B
inv_b = det != 0 ? -b / det : 0Inv C
inv_c = det != 0 ? -c / det : 0Inv D
inv_d = det != 0 ? a / det : 0Variables
| Variable | Description | Default |
|---|---|---|
a | a (row 1, col 1) | 4 |
b | b (row 1, col 2) | 7 |
c | c (row 2, col 1) | 2 |
d | d (row 2, col 2) | 6 |
det | Derived value= a * d - b * c | calculated |
How It Works
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)
Worked Example
Find the inverse of [[4, 7], [2, 6]].
a = 4b = 7c = 2d = 6
- 01det = 4×6 - 7×2 = 24 - 14 = 10
- 02Inverse = (1/10) × [[6, -7], [-2, 4]]
- 03= [[0.6, -0.7], [-0.2, 0.4]]
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