Matrix Inverse Calculator

Calculate the inverse of a 2×2 matrix, if it exists.

Inv A

0.600000

Determinant10.0000
Inv B-0.700000
Inv C-0.200000

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)

Example Calculation

Find the inverse of [[4, 7], [2, 6]].

  1. 01det = 4×6 - 7×2 = 24 - 14 = 10
  2. 02Inverse = (1/10) × [[6, -7], [-2, 4]]
  3. 03= [[0.6, -0.7], [-0.2, 0.4]]

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