Matrix Inverse Calculator
Choose the size and enter each row of the matrix.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- 2×2: inverse = 1 ÷ det × [[d, −b], [−c, a]]
- 3×3: inverse = 1 ÷ det × the transpose of the matrix of cofactors
- The determinant must not be 0
For the determinant alone, use the matrix determinant calculator.
Worked example
The matrix with rows 4, 7 / 2, 6:
- det = 24 − 14 = 10
- Inverse = [[0.6, −0.7], [−0.2, 0.4]]
Why your number may differ
Values are rounded to 6 decimal places, so a product with the original may show tiny rounding differences.
Frequently asked questions
What is the inverse of a matrix?
The matrix that, multiplied by the original, gives the identity matrix. It is like the reciprocal of a number.
How is a 2×2 inverse found?
For [[a, b], [c, d]], swap a and d, change the signs of b and c, and divide everything by the determinant ad − bc.
When is there no inverse?
When the determinant is 0. Such a matrix is called singular.