Mathematics is the queen of the sciences.C. F. Gauss

OONONNOO

2×2 matrix

Determinant, trace, norm and inverse of a 2×2 matrix.

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Formulas

det⁡A=a11a22−a12a21\det A=a_{11}a_{22}-a_{12}a_{21}tr⁡A=a11+a22\operatorname{tr}A=a_{11}+a_{22}∣∣A∣∣F=∑aij2||A||_F=\sqrt{\sum a_{ij}^2}A11−1=a22/det⁡AA^{-1}_{11}=a_{22}/\det AA12−1=−a12/det⁡AA^{-1}_{12}=-a_{12}/\det AA21−1=−a21/det⁡AA^{-1}_{21}=-a_{21}/\det AA22−1=a11/det⁡AA^{-1}_{22}=a_{11}/\det A

How it works

Determinant, trace, norm and inverse of a 2×2 matrix.