LaTeX
A^{-1}=\frac1{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}Variables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Computes the inverse of a nonsingular two-by-two matrix.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the inverse of a 2×2 matrix with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Inverse of a 2×2 Matrix, verify assumptions and units before applying the expression.
- For the Inverse of a 2×2 Matrix, 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
Use the inverse of a 2×2 matrix with a small known example, then verify the result independently.
Common mistakes
- When copying Inverse of a 2×2 Matrix, 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 Inverse of a 2×2 Matrix 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}=\frac1{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 Inverse of a 2×2 Matrix used for?
Computes the inverse of a nonsingular two-by-two matrix.
Can I copy this formula as LaTeX?
Yes. Copy A^{-1}=\frac1{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.