Matrix Inverse

About this calculator

The Matrix Inverse Calculator inverts a square matrix by Gauss-Jordan elimination on the augmented system [A | I], reducing the left block to the identity so the right block becomes A⁻¹. Partial pivoting keeps the elimination stable, and every step runs in 30-digit decimal arithmetic, so rational inputs give exact answers. It reports the determinant, the full inverse, and the verification product A·A⁻¹ (which should be the identity), and cleanly flags singular matrices — determinant 0 — as having no inverse.

How to use the Matrix Inverse calculator

1. Enter the values for your problem into the input fields.
2. Read the result — it updates instantly as you type.
3. Check the formula and the visual explanation to follow how the answer was found.
4. Copy the page URL to share the exact calculation.

Common examples

• [[2, 1], [1, 1]] → det = 1, inverse [[1, −1], [−1, 2]]
• [[1,2,3],[0,1,4],[5,6,0]] → det = 1, inverse [[−24,18,5],[20,−15,−4],[−5,4,1]]
• [[4, 7], [2, 6]] → det = 10, inverse [[0.6, −0.7], [−0.2, 0.4]]
• [[1, 2], [2, 4]] → det = 0, singular: no inverse exists