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2×2 Matrix Calculator – Determinant, Inverse, Transpose

Determinant, inverse, transpose, and scalar multiplication of 2×2 matrices.

Inputs

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Result

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How it works

The formula behind this calculator.

det = ad − bc; inv = (1/det)·[[d,−b],[−c,a]]

A 2×2 matrix has an inverse only if its determinant is non-zero. The inverse is the matrix of cofactors divided by the determinant.

Example: For [[3,8],[4,6]]: det = 18 − 32 = −14; inv = −1/14 · [[6,−8],[−4,3]]

Ref: Linear algebra, 2×2 special case

Tips

💡 A matrix has no inverse when its determinant is 0. The system then has either no solutions or infinitely many.
💡 Use a different method (e.g. Cramer's rule, row reduction) for non-2x2 systems.

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