Math

Free Matrix Calculator (2×2)

Determinant and inverse of a 2×2 matrix.

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Inputs

Result

Determinant

-2.000

Inverse[[-2.000, 1.000], [1.500, -0.500]]
Trace5.000

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Short answer

Determinant and inverse of a 2×2 matrix.

What is the Matrix Calculator (2×2)?

Determinant and inverse of a 2×2 matrix.

How does the Matrix Calculator (2×2) work?

Enter the inputs above and read the result.

Formula

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

Variables

  • a,b,c,dMatrix entries

Explanation

Standard 2×2 determinant and inverse.

Examples

Applications

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          Tips

            Related concepts

            The Matrix Calculator (2×2) sits inside the Math Calculators hub, in the number tools & notation cluster. Bases, factors, rounding and precision. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            basefactornotationprecisioninteger

            Practical use cases and industry applications

            Understanding Matrix (2×2)

            Determinant and inverse of a 2×2 matrix. Within math calculators, matrix (2×2) belongs to the number tools & notation cluster, where it shares terminology and assumptions with closely related tools.

            Learning how matrix (2×2) is calculated

            Standard 2×2 determinant and inverse. Working through the variables one at a time — a,b,c,d — makes the result reproducible by hand and easier to sanity-check.

            Using matrix (2×2) to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How matrix (2×2) compares with related measures

            base, factor, notation, precision all describe adjacent aspects of number tools & notation. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

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