CALCULATOR
Invertible [[a,b],[-b,d]] Matrix Inverse Entry Calculator
Invertible [[a,b],[-b,d]] Matrix Inverse Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 2 number, B: 1 number, D: 3 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 0.428571428571 number. Only displayed positive-diagonal skew-offdiagonal 2×2 family; no arbitrary singular-matrix admission. Original useful product scope
Only displayed positive-diagonal skew-offdiagonal 2×2 family; no arbitrary singular-matrix admission. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Positive diagonal a,d guarantees ad+b²≥0.01; inverse follows adjugate identity.
Accepted inputs: A: 0.1 to 100 number; B: -100 to 100 number; D: 0.1 to 100 number; Entry: 0=11, 1=12, 2=21, 3=22: choose Row 1, column 1 (0), Row 1, column 2 (1), Row 2, column 1 (2), Row 2, column 2 (3).
How the calculation works
A⁻¹=[[d,-b],[b,a]]/(ad+b²)
Worked example
With a 2 number, b 1 number, d 3 number, entry: 0=11, 1=12, 2=21, 3=22 Row 1, column 1, invertible [[a,b],[-b,d]] matrix inverse entry is 0.4285714286 number.
Assumptions and limits
Only displayed positive-diagonal skew-offdiagonal 2×2 family; no arbitrary singular-matrix admission. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Positive diagonal a,d guarantees ad+b²≥0.01; inverse follows adjugate identity.