LaTeX
A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}Variables
- a,b,c,d: matrix entries
How to use this formula
Finds the inverse of a nonsingular 2×2 matrix.
Important notes
- The determinant ad−bc must be nonzero.
Quick example
Check by multiplying A A⁻¹=I.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The determinant ad−bc must be nonzero.
- For the Two by Two Matrix Inverse, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Preserve matrix order and verify dimension compatibility; multiplication and inversion are not generally commutative or always defined.
- Matrix and vector dimensions must be compatible, and any required inverse, determinant, rank, or basis condition must hold.
Worked example
Check by multiplying A A⁻¹=I.
Common mistakes
- When copying Two by Two Matrix Inverse, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not assume commutativity, invertibility, independence, or full rank unless the required condition has been established.
Continue the workflow
Use Two by Two Matrix Inverse in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Two by Two Matrix Inverse used for?
Finds the inverse of a nonsingular 2×2 matrix.
Can I copy this formula as LaTeX?
Yes. Copy A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.