Inverse matrix calculator
Type a square matrix, one row per line, and get its inverse A⁻¹ as exact fractions or as decimals, together with the determinant.
One row per line, numbers separated by spaces. Fractions such as 1/2 are allowed.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How it works
The matrix is extended with the identity matrix and reduced with row operations (Gauss-Jordan) until the left half is the identity. The right half is then A⁻¹. As a check, A × A⁻¹ gives the identity matrix.
For a 2×2 matrix [[a, b], [c, d]] there is a shortcut: A⁻¹ = 1/(ad − bc) · [[d, −b], [−c, a]].
No inverse?
A matrix with determinant 0 has no inverse, because its rows are dependent. You get a message instead of a result. Fractions stay exact by default; switch to decimals if you prefer. For just the determinant, use the determinant calculator.
Frequently asked questions
Is the inverse matrix calculator free?
Yes. The inverse matrix calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.