Matrix Calculator
Determinant, inverse, transpose and adjugate of 2 × 2 and 3 × 3 matrices.
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How to use this calculator
Choose the size, enter the numbers in the grid, and choose an operation. Answers are exact fractions where needed.
How it's calculated
2 × 2 determinant: ad − bc. 3 × 3: expand along the first row. Inverse = (1 ÷ det) × adjugate, where the adjugate is the transpose of the cofactor matrix. A matrix has an inverse only if its determinant is not 0.
Worked example
For [[1, 2], [3, 4]]: det = 1×4 − 2×3 = −2, and the inverse is [[−2, 1], [3/2, −1/2]].
Frequently asked questions
When does a matrix have no inverse?
When its determinant is 0. It is then called singular.
What is the adjugate?
The transpose of the matrix of cofactors. Dividing it by the determinant gives the inverse.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.